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Circular Motion amp Gravity
Circular Motion
bull Objects travel in a circlebull Rotate about an axis of rotation
bull Tangential speed (vt) describes the rate at which the object moves around the circle
bull Direction is tangential to the circular path
period
ncecircumfere2
T
rvt
vt depends upon radius
bull Given the object is rigid eg a CD
bull Object B must travel a greater distance to keep up with object A
bull SB gt SA
bull But ΔtB = ΔtA
bull Therefore vB gt vA
Comparison of Translational Motion amp Uniform Circular Motion
UCM = motion of an object traveling in a circle at a constant speed vt
Type of Motion TranslationalUniform Circular
DisplacementLinear
Δx
Circumference
2πr
Time ΔtPeriod
T
Formula vavg = ΔxΔt vt = 2πrT
Uniform Circular Motion
bull Tangential speed vt is constant
bull Because direction is changing there is acceleration
bull Centripetal acceleration
Centripetal Acceleration
bull a = ΔvΔt
bull When subtracting vectors reverse the direction of vi
bull Centripetal acceleration is therefore directed toward the center (axis of rotation) when θ is small
Centripetal Acceleration
bull Centripetal means ldquocenter seekingrdquo and is always directed toward the center
bull Due to a change in direction of vt
bull Phet simulationr
va t
c
2
Tangential Acceleration
bull Tangential acceleration occurs when there is a change in tangential speed
bull For example if a car is speeding up as it goes around a curvendash It has tangential
acceleration andndash Centripetal acceleration
Centripetal Force
Because Fc acts at right angles to the objectrsquos circular motion it changes the direction of the objects velocity
Centripetal Force
bull Is the cause of centripetal acceleration
bull It is directed toward the axis of rotation
bull It is the net force acting on an object in uniform circular motion ie it is the cause of circular motion
bull CentrifugalCentrifugal force is a misunderstanding force is a misunderstanding of inertiaof inertia
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Circular Motion
bull Objects travel in a circlebull Rotate about an axis of rotation
bull Tangential speed (vt) describes the rate at which the object moves around the circle
bull Direction is tangential to the circular path
period
ncecircumfere2
T
rvt
vt depends upon radius
bull Given the object is rigid eg a CD
bull Object B must travel a greater distance to keep up with object A
bull SB gt SA
bull But ΔtB = ΔtA
bull Therefore vB gt vA
Comparison of Translational Motion amp Uniform Circular Motion
UCM = motion of an object traveling in a circle at a constant speed vt
Type of Motion TranslationalUniform Circular
DisplacementLinear
Δx
Circumference
2πr
Time ΔtPeriod
T
Formula vavg = ΔxΔt vt = 2πrT
Uniform Circular Motion
bull Tangential speed vt is constant
bull Because direction is changing there is acceleration
bull Centripetal acceleration
Centripetal Acceleration
bull a = ΔvΔt
bull When subtracting vectors reverse the direction of vi
bull Centripetal acceleration is therefore directed toward the center (axis of rotation) when θ is small
Centripetal Acceleration
bull Centripetal means ldquocenter seekingrdquo and is always directed toward the center
bull Due to a change in direction of vt
bull Phet simulationr
va t
c
2
Tangential Acceleration
bull Tangential acceleration occurs when there is a change in tangential speed
bull For example if a car is speeding up as it goes around a curvendash It has tangential
acceleration andndash Centripetal acceleration
Centripetal Force
Because Fc acts at right angles to the objectrsquos circular motion it changes the direction of the objects velocity
Centripetal Force
bull Is the cause of centripetal acceleration
bull It is directed toward the axis of rotation
bull It is the net force acting on an object in uniform circular motion ie it is the cause of circular motion
bull CentrifugalCentrifugal force is a misunderstanding force is a misunderstanding of inertiaof inertia
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
vt depends upon radius
bull Given the object is rigid eg a CD
bull Object B must travel a greater distance to keep up with object A
bull SB gt SA
bull But ΔtB = ΔtA
bull Therefore vB gt vA
Comparison of Translational Motion amp Uniform Circular Motion
UCM = motion of an object traveling in a circle at a constant speed vt
Type of Motion TranslationalUniform Circular
DisplacementLinear
Δx
Circumference
2πr
Time ΔtPeriod
T
Formula vavg = ΔxΔt vt = 2πrT
Uniform Circular Motion
bull Tangential speed vt is constant
bull Because direction is changing there is acceleration
bull Centripetal acceleration
Centripetal Acceleration
bull a = ΔvΔt
bull When subtracting vectors reverse the direction of vi
bull Centripetal acceleration is therefore directed toward the center (axis of rotation) when θ is small
Centripetal Acceleration
bull Centripetal means ldquocenter seekingrdquo and is always directed toward the center
bull Due to a change in direction of vt
bull Phet simulationr
va t
c
2
Tangential Acceleration
bull Tangential acceleration occurs when there is a change in tangential speed
bull For example if a car is speeding up as it goes around a curvendash It has tangential
acceleration andndash Centripetal acceleration
Centripetal Force
Because Fc acts at right angles to the objectrsquos circular motion it changes the direction of the objects velocity
Centripetal Force
bull Is the cause of centripetal acceleration
bull It is directed toward the axis of rotation
bull It is the net force acting on an object in uniform circular motion ie it is the cause of circular motion
bull CentrifugalCentrifugal force is a misunderstanding force is a misunderstanding of inertiaof inertia
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Comparison of Translational Motion amp Uniform Circular Motion
UCM = motion of an object traveling in a circle at a constant speed vt
Type of Motion TranslationalUniform Circular
DisplacementLinear
Δx
Circumference
2πr
Time ΔtPeriod
T
Formula vavg = ΔxΔt vt = 2πrT
Uniform Circular Motion
bull Tangential speed vt is constant
bull Because direction is changing there is acceleration
bull Centripetal acceleration
Centripetal Acceleration
bull a = ΔvΔt
bull When subtracting vectors reverse the direction of vi
bull Centripetal acceleration is therefore directed toward the center (axis of rotation) when θ is small
Centripetal Acceleration
bull Centripetal means ldquocenter seekingrdquo and is always directed toward the center
bull Due to a change in direction of vt
bull Phet simulationr
va t
c
2
Tangential Acceleration
bull Tangential acceleration occurs when there is a change in tangential speed
bull For example if a car is speeding up as it goes around a curvendash It has tangential
acceleration andndash Centripetal acceleration
Centripetal Force
Because Fc acts at right angles to the objectrsquos circular motion it changes the direction of the objects velocity
Centripetal Force
bull Is the cause of centripetal acceleration
bull It is directed toward the axis of rotation
bull It is the net force acting on an object in uniform circular motion ie it is the cause of circular motion
bull CentrifugalCentrifugal force is a misunderstanding force is a misunderstanding of inertiaof inertia
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Uniform Circular Motion
bull Tangential speed vt is constant
bull Because direction is changing there is acceleration
bull Centripetal acceleration
Centripetal Acceleration
bull a = ΔvΔt
bull When subtracting vectors reverse the direction of vi
bull Centripetal acceleration is therefore directed toward the center (axis of rotation) when θ is small
Centripetal Acceleration
bull Centripetal means ldquocenter seekingrdquo and is always directed toward the center
bull Due to a change in direction of vt
bull Phet simulationr
va t
c
2
Tangential Acceleration
bull Tangential acceleration occurs when there is a change in tangential speed
bull For example if a car is speeding up as it goes around a curvendash It has tangential
acceleration andndash Centripetal acceleration
Centripetal Force
Because Fc acts at right angles to the objectrsquos circular motion it changes the direction of the objects velocity
Centripetal Force
bull Is the cause of centripetal acceleration
bull It is directed toward the axis of rotation
bull It is the net force acting on an object in uniform circular motion ie it is the cause of circular motion
bull CentrifugalCentrifugal force is a misunderstanding force is a misunderstanding of inertiaof inertia
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Centripetal Acceleration
bull a = ΔvΔt
bull When subtracting vectors reverse the direction of vi
bull Centripetal acceleration is therefore directed toward the center (axis of rotation) when θ is small
Centripetal Acceleration
bull Centripetal means ldquocenter seekingrdquo and is always directed toward the center
bull Due to a change in direction of vt
bull Phet simulationr
va t
c
2
Tangential Acceleration
bull Tangential acceleration occurs when there is a change in tangential speed
bull For example if a car is speeding up as it goes around a curvendash It has tangential
acceleration andndash Centripetal acceleration
Centripetal Force
Because Fc acts at right angles to the objectrsquos circular motion it changes the direction of the objects velocity
Centripetal Force
bull Is the cause of centripetal acceleration
bull It is directed toward the axis of rotation
bull It is the net force acting on an object in uniform circular motion ie it is the cause of circular motion
bull CentrifugalCentrifugal force is a misunderstanding force is a misunderstanding of inertiaof inertia
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Centripetal Acceleration
bull Centripetal means ldquocenter seekingrdquo and is always directed toward the center
bull Due to a change in direction of vt
bull Phet simulationr
va t
c
2
Tangential Acceleration
bull Tangential acceleration occurs when there is a change in tangential speed
bull For example if a car is speeding up as it goes around a curvendash It has tangential
acceleration andndash Centripetal acceleration
Centripetal Force
Because Fc acts at right angles to the objectrsquos circular motion it changes the direction of the objects velocity
Centripetal Force
bull Is the cause of centripetal acceleration
bull It is directed toward the axis of rotation
bull It is the net force acting on an object in uniform circular motion ie it is the cause of circular motion
bull CentrifugalCentrifugal force is a misunderstanding force is a misunderstanding of inertiaof inertia
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Tangential Acceleration
bull Tangential acceleration occurs when there is a change in tangential speed
bull For example if a car is speeding up as it goes around a curvendash It has tangential
acceleration andndash Centripetal acceleration
Centripetal Force
Because Fc acts at right angles to the objectrsquos circular motion it changes the direction of the objects velocity
Centripetal Force
bull Is the cause of centripetal acceleration
bull It is directed toward the axis of rotation
bull It is the net force acting on an object in uniform circular motion ie it is the cause of circular motion
bull CentrifugalCentrifugal force is a misunderstanding force is a misunderstanding of inertiaof inertia
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Centripetal Force
Because Fc acts at right angles to the objectrsquos circular motion it changes the direction of the objects velocity
Centripetal Force
bull Is the cause of centripetal acceleration
bull It is directed toward the axis of rotation
bull It is the net force acting on an object in uniform circular motion ie it is the cause of circular motion
bull CentrifugalCentrifugal force is a misunderstanding force is a misunderstanding of inertiaof inertia
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Centripetal Force
bull Is the cause of centripetal acceleration
bull It is directed toward the axis of rotation
bull It is the net force acting on an object in uniform circular motion ie it is the cause of circular motion
bull CentrifugalCentrifugal force is a misunderstanding force is a misunderstanding of inertiaof inertia
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Centripetal Force amp Newtonrsquos 2nd Law
r
vmF
r
vamaF
maF
tc
tccc
2
2
Since
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Centripetal Force
bull Is just the name of any net force acting on an object in uniform circular motion
bull Fc could take any formhellip
bull It could be frictional force tension force gravitational force etc
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Motion of a Car Around a Curve
bull On a horizontal turn the centripetal force is friction
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Circular Motion About a Banked Curve
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Conical Pendulum
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Vertical Circular Motion
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Centifugal Force
bull If Fc is insufficient to maintain circular motion the object will leave itrsquos circular path due to its own inertia not because some force is pulling it away from the axis of rotation
bull Thus inertia is often mistaken for ldquocentrifugal forcerdquo
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Gravity
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Gravitational Force
bull Force of attraction between two masses
bull Attractive only
bull One of four fundamental forces
bull Very weak (the weakest)
bull When one object orbits another gravitational force is a centripetal force
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Newtonrsquos Law of Universal Gravitation
bull Gravitational force ishellipndash directly proportional to the product of the masses of
the two bodiesndash inversely proportional to the square of the distance
between the centers of the two massesndash If the objects are large (eg planets moons) then the
radii would be included in r
2
211
221
kg
mN106736constantn gravitatio universal
GG
r
mmGFg
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Gravitational Force Exists Between Any Two Masses
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Newtonrsquos Cannon
httpspaceplacenasagovenkidsorbits1shtmlhttpgalileoandeinsteinphysicsvirginiaedumore_stuffAppletsnewtnewtmtnhtml
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Importance of Gravitational Force
bull Keeps you from floating away into space
bull Gravitational force keeps the Moon and planets in orbit
bull Keeps earth in orbit around sun
bull Causes ocean tides
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Black Holes Extreme GravityExtreme density
Escape velocity gt speed of light
Detect by effects on surrounding matter
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
bull Increases as distance from mass center decreases
bull Because gravitational field strength varies weight varies with location
Gravitational Field Strength
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Gravitational Field Strength
bull Describes the amount of gravitational force per unit mass at any given point
bull Equals free-fall acceleration
m
Fg g
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Weight Changes with Location
bull Because gravitational field strength varies ag varies (acceleration of gravity)
bull Since w = mag weight must vary as ag varies
bull Fg is an example of an inverse square law
221
r
mmGFg
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
73 Motion in Space
Astronomer Planets orbithellip
Type of orbit
Ptolomey Earth Epicycles
Copernicus Sun Circular
Kepler Sun Elliptical
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Keplerrsquos Laws of Planetary Motion
1 The Law of Orbits All planets move in elliptical orbits with the sun at one focus
2 The Law of Areas A line that connects a planet to the sun sweeps out equal areas in equal times
3 The Law of Periods The square of the period of any planet is proportional to the cube of the average distance from the sun
32 rT
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Keplerrsquos 1st and 2nd Laws
Keplers Law Simulation
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Keplerrsquos 3rd Law Describes Orbital Period
mass theof mass theis re whe
2
speed Orbital Period Orbital
in object an of speed and Period
3
orbitedmr
mGv
Gm
rT
rbitCircular O
t
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Actual and Apparent Weightbull A bathroom scale records the normal force
of scale acting on your body
bull Step on the scale hellip the normal force equals your weight
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Actual and Apparent Weight
bull Now try this
bull Step on the scale and have someone press down on your shouldersndash Predict and explain the result
bull Step on the scale and have someone lift you slightly
bull Predict and explain the result
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Actual and Apparent Weight
bull How does this relate to your experiences in an elevator
bull What would the scale read if in an elevator it descended with an acceleration of g
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Weight and Apparent Weightlessness
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Torque
bull a quantity that measures the ability of a force to rotate an object about an axis
bull is not a force
bull ldquorotating abilityrdquo
bull the product of force and ldquolever armrdquobull τ = F d sinθ
bull Lever arm (d) is distance perpendicular to direction of force to axis of rotation
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
sinFd
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Torque
bull Sign (+) is counterclockwise
(-) is clockwise
bull Net Torque and
when 2 or more forces act to rotate the same object τnet = Στ
τnet = τ1 + τ2 = F1d1 + F2d2
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Torque Equilibrium
bull Torque Equilibrium Στ = 0
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Torque EquilibriumThe torque due to the boy is equal and opposite to that of the girl
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Net Torque
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Center of Mass (COM)
bull Point mass vs extended object
bull The point in a body at which all the mass can be considered to be concentrated when analyzing translational motion
bull Unless an object rotates about a fixed point (eg a hinge)hellipndash The point about which a mass or system of
mass rotates during rotational motion
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Center of Mass
bull The extended object rotates about the CoM
bull CoM follows the expected parabolic path
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Center of Mass
bull May not lie within the mass or system of masses
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Simple Machines
bull All machines are combinations of simple machinesbull Purpose is to change magnitude or direction of an
input forcebull Mechanical Advantage
describes the ratio of output and input forces
in
out
F
FMA
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Ideal vs Actual Mechanical Advantage
bull Ideal MA
MA if there were no friction
bull Actual MA
MA that takes friction into account
out
in
d
dIMA
in
out
F
FAMA
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Machines and Workbull Machines do not change the amount of workbull Machines make work easier
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
Efficiency
bull A measure of how well a machine worksbull A less efficient machine produces less output
per inputbull A less efficient machine requires more input
to get the same output
in
out
W
Weff
