Physics C Equations Sheet - College Board

ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION

CONSTANTS AND CONVERSION FACTORS

Proton mass, = mp 1.67 ? 1027 kg Electron charge magnitude, =e 1.60 ? 1019 C

Neutron mass, = mn 1.67 ? 1027 kg

1 electron volt, 1= eV 1.60 ? 1019 J

Electron mass, = me 9.11 ? 1031 kg Avogadro's number, = N0 6.02 ? 1023 mol1

. Universal gas constant, R 8.31 JI(mol K)

Speed of light, =c 3.00 ? 108 mIs

. I Universal gravitational constant,

= G

6.67 ? 1011 N m2

kg2

I Acceleration due to gravity at Earth's surface,

g 9.8 m s2

Boltzmann's constant, = kB 1.38 ? 1023 JIK

1 unified atomic mass unit,

I 1 u = 1.66 ? 1027 kg = 931 MeV c2

Planck's constant,

. . h = 6.63 ? 1034 J s = 4.14 ? 1015 eV s

. . hc = 1.99 ? 1025 J m = 1.24 ? 103 eV nm

Vacuum permittivity,

I . = e0 8.85 ? 1012 C2 N m2

. I I Coulomb's law constant, =k 1 4pe= 0 9.0 ? 109 N m2 C2

Vacuum permeability,

. m=0 4p ? 107 (T m)IA

. Magnetic constant, k?= m0 I4p= 1 ? 107 (T m)IA

1 atmosphere pressure,

I 1 atm = 1.0 ? 105 N m2 = 1.0 ? 105 Pa

meter, m

UNIT SYMBOLS

kilogram, second, ampere,

kg s A

kelvin, K

mole, mol

hertz, Hz

newton, N

pascal, Pa

joule,

J

watt, coulomb,

volt, ohm, henry,

w

farad,

F

C

tesla,

T

V degree Celsius, ?C

W

electron volt,

eV

H

PREFIXES

Factor Prefix Symbol

109

giga

G

106

mega

M

103

kilo

k

102

centi

C

103

milli

m

106

micro

m

109

nano

n

1012

pico

p

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

q

0

30

37

45

53

60

90

sin q

0

1I2 3I5 r2;2 4I5 r3;2

1

cosq

1 r3;2 4I5 r2;2 3I5 1I2

0

tan q

0 r3;3 3I4

1

4I 3

3

?

The following assumptions are used in this exam. I. The frame of reference of any problem is inertial unless otherwise stated. II. The direction of current is the direction in which positive charges would drift.

III. The electric potential is zero at an infinite distance from an isolated point charge.

IV. All batteries and meters are ideal unless otherwise stated. V. Edge effects for the electric field of a parallel plate capacitor are

negligible unless otherwise stated.

164|AppendixV.1

AP Physics C: MechanicsCourse and Exam Description

ADVANCED PLACEMENT PHYSICS C EQUATIONS

MECHANICS

ELECTRICITY AND MAGNETISM

?x ?x0 axt

x

x0

?x0 t

1 2

axt

2

?x2 ?x02 2ax x x0

a

? mF

Fnet m

a = acceleration

E= energy F= force f = frequency

h = height

I = rotational inertia

J = impulse

K= kinetic energy

FE

1 4pe0

q1q2 r 2

E

FE q

?E

dA

Q e0

A= area B= magnetic field

C= capacitance

d = distance

E= electric field

e = emf

F= force

I = current

F

dp dt

k = spring constant ? = length L = angular momentum

Ex

dV dx

J = current density

L = inductance = length

? J F dt Dp

m= mass P= power

DV ? E dr

n = number of loops of wire per unit length

p mv

IF-f I? m1F~N I

? D E W F d r

p = momentum

r = radius or distance

T= period

t = time

U= potential energy

v = velocity or speed

? V

1 4pe0

i

qi r i

U E

q V

1 q1q2 4pe0 r

N= number of charge carriers

per unit volume

P= power Q= charge

q = point charge

R= resistance

K

1 2

m?2

P

dE dt

W= work done on a system x = position m = coefficient of friction

q = angle t = torque

DV

Q C

C

k e0 A d

PF v DUg mgDh ac ? r2 w2r t= r ? F

w = angular speed a = angular acceleration f = phase angle

Fs kDx

Us

1 2

k

Dx

2

Cp ?Ci i

1 Cs

?

i

1 Ci

I

dQ dt

a

? It

tnet I

x xmax cos(wt f

T

2 wp

1 f

? I r2dm ? mr2

xcm

? mi xi ? mi

? rw

L = r ? p = Iw

F Ts 2p

m k

f Tp 2p g

I- IFG

Gm1m2 r 2

K

1 2

I

w2

UG

Gm1m2 r

w w0 at

UC 12 QDV

R

re

A

E rJ

I Nevd A

I

DV R

Rs

? Ri

i

1 Rp

?

i

1 Ri

r = radius or distance

t = time

U= potential or stored energy V = electric potential

v = velocity or speed r = resistivity

F = flux

k = dielectric constant

FM= qv ? B

.?0 B- d ? m0I

1 2

C

DV

2

dB

m0 4p

I d ?? r 2

r

= F ? I d ? ? B

Bs m0nI

.? FB B dA

. ? e

0

E-

d?

dFB dt

e

L

dI dt

UL

1 2

LI

2

q

q0

w0t

1 2

at

2

P I DV

-2-

AP Physics C: MechanicsCourse and Exam Description

AppendixV.1|165

ADVANCED PLACEMENT PHYSICS C EQUATIONS

GEOMETRY AND TRIGONOMETRY

Rectangle

A bh

Triangle

A

1 2

bh

Circle

A pr2

C 2pr

s rq

Rectangular Solid

V f wh

Cylinder V pr2

S 2pr 2pr2

Sphere

V

4 3

p

r3

S 4pr2

A =area C =circumference V =volume S = surface area b =base h =height = length w =width r =radius s = arc length q = angle

q

Right Triangle

a2 b2 c2

sin q

a c

cosq

b c

tan q

a b

~ ~ a b

CALCULUS

df dx

df du

du dx

d

dx

xn

nxn 1

d

dx

eax

aeax

d dx

ln

ax

1 x

d dx

sin

ax

a cosax

d dx

cos ax

a sin ax

? = xn dx

n

1

1

xn 1,

n

?

-1

? eax dx

1 a

eax

? x d xa ln x a

? cosax dx

1 a

sin

ax

? sinax dx

1 a

cos

ax

VECTOR PRODUCTS A?B AB cosq A ? B = ABsinq

166|AppendixV.1

AP Physics C: MechanicsCourse and Exam Description

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