Chapter 9

Circular Motion

PeriodThe time it takes for 1 full rotation of an object.

T = 1/ƒ

Period = 1/frequency

s = 1/Hz

How long??

?

Frequency

The number of rotations per unit of time.

Measured in Hz. (Hertz)

How many?

?

Linear (Tangential) SpeedWhen an object spins in a circle…

distance = circumference

vc = 2πr T

Linear speed = 2π * radius Period

m/s = m s

Please note…

An object can move around a circle with a CONSTANT SPEED, yet still be accelerating!

How?????????

Because its direction is

always changing!

Centripetal Acceleration

Always directed toward the center of the circle.

ac = v2

rCentripetal acc = (linear speed)2

radius

m/s2 = m/s

m

Centripetal ForceAlways directed toward the center of the circle.

Fc = mac

Centripetal force = mass * centripetal acc.

N = kg * m/s2

Example 1After closing a deal with a client, Kent leans back in his swivel chair and spins around with a frequency of 0.5 Hz. What is Kent’s period of spin?

T = 1/ƒ

2 s

Example 2Curtis’ favorite disco record has a scratch 0.12 m from the center that makes the record skip 45 times each minute. What is the linear speed of the scratch as it turns?

1st find the period: T = 1/f

T = 1.3 s

2nd find the linear speed: v = 2πr/T

V = .58 m/s

Example 3Missy’s favorite ride at the fair is the rotor, which has a radius of 4.0 m. The ride takes 2.0 s to make one full revolution.

What is Missy’s linear speed?

v = 2πr/T

v = 13 m/s

What is Missy’s centripetal acceleration?

ac = v2/r

ac = 42 m/s2

Example 4Captain Chip pilots a 60,500 kg plane. He must circle above the airport to wait his turn to land. If Chip flies his plane in a circle whose radius is 50,000. m every 1,800. s, what centripetal force must the air exert against the wings to keep the plane moving in a circle?

First, find the speed: v = 2πr/T

v = 175.0 m/s

Next find centripetal force: Fc = mv2/r

Fc = 37,100 N

Abby

A ball on a string is swung in a circle. The string breaks.

Which trajectory does the ball follow?

A?

B?

C?

D?C. The line that is tangent!!

Ball on a string

The tension in the stringprovides the necessarycentripetal force to keep the ball going in a circle.

path of ball if the stringbreaks

The force required to cause an object to follow a circular path.

Centripetal means “center seeking”

Centripetal Force

The net force is towards

the center!

A car turning a corner…MUST have a centripetal force in order to put it into a circular path!

Friction between the road and tires is the centripetal force.

No friction (ice) = No centripetal force This makes the car slide.

Centrifugal forceCentrifugal means “center fleeing.” The red object will make the turn only if there is enough friction on it…otherwise it goes straight.

The apparent outward force is called the centrifugal force…

But it isn’t a force at all-But it isn’t a force at all-it’s actually the it’s actually the absenceabsence of a centripetal force!!!of a centripetal force!!!

object onthe dashboard

straight lineobject naturally

follows

Silly Silo (Rotor)

Bart’sweight

Friction betweenBart and wall

wall pushing in on Bart

The inward wall force keeps Bart in the circle.Friction keeps him from falling down.

6-Dec-05Earth orbitVery little gravity in space…

Very little gravity in space…

But we can make our own to make it

easier!

The International Space Station

The faster it rotates, the more people will weigh.

Ladybug on the inside of a bike tire…

Just like the space station, it would feel like gravity for the ladybug!!!

The faster the bike goes, the more the ladybug will weigh!

Ladybug on a TurntableWhich ladybug has a greater velocity?

a. The inside ladybug.

b. The outside ladybug.

B. The outside ladybug!

Why???It must cover more distance in the same amount of time!

Basically, the velocity depends on the radius.

Larger radius = larger velocity!

Smaller radius = smaller velocity!

Lab Set Up

tape

Goal: The weight (N) hanging down = the Centripetal Force (N)