physics equations

TABLE OF INFORMATION FOR 2002

CONSTANTS AND CONVERSION FACTORS

1 unified atomic mass unit, 1 u 1 66 1027

=

=

-

. 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 ¼8 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 = ¼

-

6 67 1011 3 2

. /m kg s

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. For mechanics and thermodynamics equations, W represents the work done on a system.

*Not on the Table of Information for Physics C, since Thermodynamics is not a Physics C topic.

x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 2

ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2002

NEWTONIAN MECHANICS ELECTRICITY AND MAGNETISM

u u

u

u u

m

u

t

q

p

p

0

0 02

20

20

2

2

2

1 22

1 2

12

2

12

12

2

2

1

at

x x t at

a x x

m

F N

ar

r

m

t

K m

U mgh

W F r

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

F x

F sin

q

u

u q

D D

D

D D

D

r

F v

cos

cos

a = accelerationF = forcef = frequencyh = heightJ = impulseK = kinetic energyk = spring constant = lengthm = massN = normal forceP = powerp = momentumr = radius or distancer = position vectorT = periodt = timeU = potential energyu = velocity or speedW = work done on a systemx = positionm = coefficient of frictionq = anglet = torque

Fq q

r

q

U qVq q

r

EV

d

Vq

r

CQ

V

CA

d

U QV CV

IQ

t

RA

V IR

P IV

C C

C C

R R

R R

F q B

F BI

BI

r

BA

t

B

E

avg

i

ii

avg

i

i

B

B

c

p ii

s ii

s i

p i

m

m

=

=

= =

= −

=

=

=

= =

=

=

==

=

=

=

=

=

=

=

= =

= −

=

∑

∑

∑

∑

∑

•

1

4

1

4

1

4

1

2

1

2

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

EF

B A

ρ

θ

θ

θ

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 2002FLUID MECHANICS ANDTHERMAL PHYSICS WAVES AND OPTICS

p p gh

F Vg

A A

p gy

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

eT T

T

buoy

avg B

rmsB

V

H

cH C

H

0

1 1 2 2

2

0

12

32

3 3

r

r

u u

r ru

m

const.

D D

D

D

D

D

D D

a

u

A = areac = specific heat or molar

specific heate = efficiencyF = forceh = depthKavg = average molecular

kinetic energyL = heat of transformation = lengthM= molecular massm = mass of samplen = number of molesp = pressureQ = heat transferred to a systemT = temperatureU = internal energyV = volumeu = velocity or speedurms = root-mean-square

velocityW = work done on a systemy = heighta = coefficient of linear

expansionµ = mass of moleculer = density

u

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

l

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

ATOMIC AND NUCLEAR PHYSICS

E hf pc

K hf

hp

E m c

= =

= −

=

=

max

( )

f

l

D D2

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

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 2002

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

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

P

U mgh

ar

r

I

I r dm mr

m m

r

I

K I

t

t t

k

U

net

g

c

net

cm

s

fric

F F a

Fp

J F pp v

F

r F

r r

L r p

F x

D

D

r

F v

t

t t a

w

s

s

p

kx

Tf

T mk

Tg

Gm m

r

UGm m

r

G

G

12

2 1

2

2

2

1 22

1 2

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 distancer = position vectorT = periodt = timeU = potential energyu = velocity or speedW = work done on a systemx = positionm = coefficient of frictionq = anglet = torquew = angular speeda = angular acceleration

Fq q

r

q

dQ

EdV

dr

Vq

r

U qVq q

r

CQ

V

CA

d

C C

C C

IdQ

dt

U QV CV

RA

V IR

R R

R R

P IV

q

d I

I d

B nI

d

d

dt

LdI

i

ii

E

i

i

M

p ii

s ii

c

s i

p i

s

m

m

=

=

=

= −

=

= =

=

=

=

=

=

= =

=

==

=

== ×

=

= ×

=

= = −

= −

•

•

•

∑

∑

∑

∑

∑

1

4

1

4

1

4

1 1

1

2

1

2

1 1

0

1 2

0

0

0

1 2

0

2

0

0

2p

p

p

k

r

m

m

f

fe

e

EF

E A

F v B

B

F B

B A

ø

ø

dt

U LIL = 1

22

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 2002

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


physics equations

Technology