TABLE OF INFORMATION FOR 2000

CONSTANTS AND CONVERSION FACTORS

1 unified atomic mass unit, 1 166 10 27u kg

931 MeV/ 2

= ×

=

−.

c

Proton mass, mp = × −1 67 10 27. kg

Neutron mass, mn = × −1 67 10 27. kg

Electron mass, me = × −9 11 10 31. kg

Magnitude of the electron charge, e = × −1 60 10 19. C

Avogadro’s number, N023 16 02 10= × −. mol

Universal gas constant, R = ⋅8 31. / ( )J mol K

Boltzmann’s constant, kB = × −138 10 23. J / K

Speed of light, c = ×3 00 108. /m s

Planck’s constant, h

hc

= ×

= ×

= ×

= ×

−

−

−

⋅⋅

⋅⋅

6 63 10

414 10

1 99 10

1 24 10

34

15

25

3

.

.

.

.

J s

eV s

J m

eV nm

Vacuum permittivity, 012 2 28 85 10= × − ⋅. /C N m

Coulomb’s law constant, k = = × ⋅1 4 9 0 1009 2 2/ . /π N m C

Vacuum permeability, µ π074 10= × − ⋅( ) /T m A

Magnetic constant, k = T m A0µ π/ ( ) /4 10 7= − ⋅Universal gravitational constant, G m kg s= × − ⋅6 67 10 11 3 2. /

Acceleration due to gravityat the Earth’s surface, g = 9 8 2. m/ s

1 atmosphere pressure,

1 1 0 10

1 0 10

5 2

5

atm N / m

Pa

= ×

= ×

.

.

1 electron volt, 1 1 60 10 19 eV J= × −.

UNITS

Name Symbol

meter m

kilogram kg

second s

ampere A

kelvin K

mole mol

hertz Hz

newton N

pascal Pa

joule J

watt W

coulomb C

volt V

ohm Ω

henry H

farad F

tesla T

degreeCelsius oC

electron-volt eV

PREFIXES

Factor Prefix Symbol

109 giga G

106 mega M

103 kilo k

10 2− centi c

10 3− milli m

10 6− micro µ

10 9− nano n

10 12− pico p

VALUES OF TRIGONOMETRIC FUNCTIONSFOR COMMON ANGLES

θ sin θ cos θ tan θ

0o 0 1 0

30o 1/2 3 2/ 3 3/

37o 3/5 4/5 3/4

45o 2 2/ 2 2/ 1

53o 4/5 3/5 4/3

60o 3 2/ 1/2 3

90o 1 0 ∞The following conventions are used in this examination.

I. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial.

II. The direction of any electric current is the direction of flow of positive charge (conventional current).

III. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge.

IV. The work done by a thermodynamic system is defined as a positive quantity.

ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2000

NEWTONIAN MECHANICS ELECTRICITY AND MAGNETISM

u u

u

u u

m

u

t

q

u

p

p

= +

= + +

= + −

∑ = =

≤

=

=

=

= =

=

=

= =

=

=

= −

=

=

=

=

= −

= −

0

0 0

0 0

2

1 22

1 2

12

2

12

12

2

2

1

2

2 2

2

2

at

x x t at

a x x

m

F N

ar

r

m

t

K m

U mgh

W Fs

P Wt

P F

k

U kx

T mk

Tg

Tf

FGm m

r

UGm m

r

net

c

s

s

p

fric

g

avg

s

G

G

F F a

p v

J F p

F s

F x

F sin q

u

D D

D

D

cos

a = accelerationF = forcef = frequencyh = heightJ = impulseK = kinetic energyk = spring constant = lengthm = massN = normal forceP = powerp = momentumr = radius or distances = displacementT = periodt = timeU = potential energyu = velocity or speedW= workx = positionm = coefficient of frictionq = anglet = torque

Fq q

r

q

U qVq q

r

E Vd

Vqr

CQV

CA

d

U QV CV

IQt

RA

V IR

P IV

C C

C C

R R

R R

F q B

F BI

B Ir

BA

t

B

E

avg

i

ii

avg

i

i

B

B

c

p ii

s ii

s i

p i

m

m

=

=

= =

= −

=

=

=

= =

=

=

=

=

=

=

=

=

=

=

=

= =

= −

=

∑

∑

∑

∑

∑

•

14

14

14

12

12

1 1

1 1

2

0

1 2

0

1 2

0

0

2

0

2p

p

p

u

m

p

f

f

u

e

e

E F

B A

D

D

D

D

r

q

q

q

sin

sin

cos

avg

A = areaB = magnetic fieldC = capacitanced = distanceE = electric fielde = emfF = forceI = current = lengthP = powerQ = chargeq = point chargeR = resistancer = distancet = timeU = potential (stored) energyV = electric potential or

potential differenceu = velocity or speedr = resistivityfm = magnetic flux

ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2000

THERMAL PHYSICS ATOMIC AND NUCLEAR PHYSICS

D D

D

D

D

D

D D

=

=

=

=

=

=

= =

=

=

= −

=

= = −

= −

a

u

0

32

3 3

T

Q mL

Q mc T

p FA

pV nRT

K k T

RTM

k T

W p V

Q nc T

U Q W

U nc T

e WQ

Q QQ

eT T

T

avg B

rmsB

V

H

H C

H

cH C

H

m

A = areac = specific heat or molar

specific heate = efficiencyKavg = average molecular

kinetic energyL = heat of transformation = lengthM= molecular massm = mass of samplen = number of molesp = pressureQ = heat transferredT = temperatureU = internal energyV = volumeurms = root-mean-square

velocityW = work done by systema = coefficient of linear

expansionµ = mass of molecule

E hf pc

K hf

hp

E m c

= =

= −

=

=

max

( )

f

l

D D2

E = energyf = frequencyK = kinetic energym = massp = momentuml = wavelengthf = work function

WAVES AND OPTICS

u l

u

q q

q

q l

l

=

=

=

=

+ =

= = −

=

=

f

n c

n n

cnn

si s f

Mhih

sis

f R

d m

xmm L

d

1 1 2 2

2

1

0

0 0

1 1 1

2

sin sin

sin

sin

d = separationf = frequency or focal

lengthh = heightL = distanceM= magnificationm = an integern = index of refractionR = radius of curvatures = distanceu = speedx = positionl = wavelengthq = angle

GEOMETRY AND TRIGONOMETRY

Rectangle

Triangle

Circle

Parallelepiped

Cylinder

Sphere

Right Triangle

A bh

A bh

A rC r

V wh

V rS r r

V r

S r

a b cacbcab

=

=

==

=

== +

=

=

+ =

=

=

=

12

2

2 2

434

2

2

2

3

2

2 2 2

p

p

p

p p

p

p

q

q

q

sin

cos

tan

A = areaC = circumferenceV = volumeS = surface areab = baseh = height = lengthw = widthr = radius

c a

b90q

ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2000

MECHANICS ELECTRICITY AND MAGNETISM

u u

u

u u

m

u

uw

u w

w

w w a

q q w a

= +

= + +

= + −∑ = =

=

= ==

≤

= =

=

=

= =

= ×∑ = =

= = ∑= ∑∑

== × =

=

= +

= + +

= −

=

•

0

0 0

0 0

0

0 0

12

2

12

12

12

12

2

2 2

2

22

2 2

2

2

at

x x t at

a x x

m

ddt

dt

m

F N

W d

K m

P dWdt

U mgh

ar

r

I

I r dm mr

m m

r

I

K I

t

t t

k

U kx

net

g

c

net

cm

s

s

fric

F F a

Fp

J F pp v

F s

r F

r r

L r p

F x

D

D

t

t t a

w

2

2 1

2

2

1 22

1 2

Tf

T mk

Tg

Gm m

r

UGm m

r

s

p

G

G

= =

=

=

= −

= −

p

w

p

p

F r

a = accelerationF = forcef = frequencyh = heightI = rotational inertiaJ = impulseK = kinetic energyk = spring constant = lengthL = angular momentumm = massN = normal forceP = powerp = momentumr = radius or distances = displacementT = periodt = timeU = potential energyu = velocity or speedW= workx = positionm = coefficient of frictionq = anglet = torquew = angular speeda = angular acceleration

Fq q

r

q

dQ

E dVdr

Vqr

U qVq q

r

CQV

CA

dC C

C C

IdQdt

U QV CV

RA

V IR

R R

R R

P IV

q

d I

Id

B nI

d

ddt

L dIdt

U

i

ii

E

i

i

M

L

p ii

s ii

c

s i

p i

s

m

m

=

=

=

= −

=

= =

=

=

=

=

=

= =

=

==

=

=

= ×

=

= ×

=

= = −

= −

•

•

•

∑

∑

∑

∑

∑

14

14

14

1 1

12

12

1 1

0

1 2

0

0

0

1 2

0

2

0

0

2p

p

p

k

r

m

m

f

fe

e

E F

E A

F v B

B

F B

B A

l

l

= 12

2LI

A = areaB = magnetic fieldC = capacitanced = distanceE = electric fielde = emfF = forceI = currentL = inductance = lengthn = number of loops of wire

per unit lengthP = powerQ = chargeq = point chargeR = resistancer = distancet = timeU = potential or stored energyV = electric potentialu = velocity or speedr = resistivityfm = magnetic fluxk = dielectric constant

ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2000

GEOMETRY AND TRIGONOMETRY

Rectangle

Triangle

Circle

Parallelepiped

Cylinder

Sphere

Right Triangle

A bh

A bh

A rC r

V wh

V rS r r

V r

S r

a b cac

bc

ab

=

=

==

=

== +

=

=

+ =

=

=

=

12

2

2 2

434

2

2

2

3

2

2 2 2

p

p

p

p p

p

p

sin

cos

tan

q

q

q

A = areaC = circumferenceV = volumeS = surface areab = baseh = height = lengthw = widthr = radius

c a

b90q

CALCULUS

dfdx

d fdu

dudx

ddx

x nx

ddx

e e

ddx

xx

ddx

x x

ddx

x x

x dxn

x n

e dx e

dxx

x

x dx x

x dx x

n n

x x

n n

x x

=

=

=

( ) =

( ) =

( ) = −

= + ≠ −

=

=

= = −

•

−

+

1

1n

1n

1

11

11

sin cos

cos sin

,

cos sin

sin cos