PHYSICS FORMULAS

1. PHYSICS FORMULAS

2. CONSTANTS AND CONVERSION FACTORS
1 unified atomic mass unit, 1 u 1 66 10
27
=
=
™
-
. kg
931 MeV/
2
c
Proton mass, mp = × −
167 10 27
. kg
Neutron mass, mn = × −
167 10 27
. kg
Electron mass, me = × −
911 10 31
. kg
Magnitude of the electron charge, e = × −
160 10 19
. C
Avogadro’s number, N0
23 1
6 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
199 10
124 10
34
15
25
3
.
.
.
.
J s
eV s
J m
eV nm
Vacuum permittivity, ⑀0
12 2 2
8 85 10= × −
⋅. /C N m
Coulomb’s law constant, k = = × ⋅1 4 9 0 100
9 2 2
/ . /π⑀ N m C
Vacuum permeability, µ π0
7
4 10= × −
⋅( ) /T m A
Magnetic constant, k
= T m A0µ π/ ( ) /4 10 7
= −
⋅
Universal gravitational constant, G = ™ ¼
-
6 67 10
11 3 2
. /m kg s
Acceleration due to gravity
at the Earth’s surface, g = 9 8 2
. m/ s
1 atmosphere pressure, 1 10 10
10 10
5 2
5
atm N/m
Pa
= ×
= ×
.
.
1 electron volt, 1 160 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
degree
Celsius o
C
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 FUNCTIONS
FOR COMMON ANGLES
θ sin θ cos θ tan θ
0
o
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
Table of Information and Equation Tables
Physics Equations

3. ADVANCED PLACEMENT PHYSICS B EQUATIONS
NEWTONIAN MECHANICS ELECTRICITY AND MAGNETISM
u u
u
u u
m
u
t
q
p
p
= +
= + +
= + -
Ê = =
ˆ
=
=
=
= =
=
=
= =
=
= =
= -
=
=
=
=
= -
= -
0
0 0
2
2
0
2
0
2
2
2
1 2
2
1 2
1
2
2
1
2
1
2
2
2
1
at
x x t at
a x x
m
F N
a
r
r
m
t
K m
U mgh
W F r
P
W
t
P F
k
U kx
T
m
k
T
g
T
f
F
Gm m
r
U
Gm m
r
net
c
s
s
p
fric
g
avg
s
G
G
0 5
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
l
a = acceleration
F = force
f = frequency
h = height
J = impulse
K = kinetic energy
k = spring constant
l = length
m = mass
N = normal force
P = power
p = momentum
r = radius or distance
r = position vector
T = period
t = time
U = potential energy
u = velocity or speed
W = work done on a system
x = position
m = coefficient of friction
q = angle
t = torque
F
q q
r
q
U qV
q q
r
E
V
d
V
q
r
C
Q
V
C
A
d
U QV CV
I
Q
t
R
A
V IR
P IV
C C
C C
R R
R R
F q B
F BI
B
I
r
BA
t
B
E
avg
i
ii
avg
i
i
B
B
c
p i
i
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
2
p
p
p
u
m
p
f
f
u
e
e
⑀
⑀
⑀
⑀
E
F
B A
D
D
D
D
ρ
θ
θ
θ
l
sin
sin
cos
l
l
avg
A = area
B = magnetic field
C = capacitance
d = distance
E = electric field
e = emf
F = force
I = current
l = length
P = power
Q = charge
q = point charge
R = resistance
r = distance
t = time
U = potential (stored) energy
V = electric potential or
potential difference
u = velocity or speed
r = resistivity
fm = magnetic flux
x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 3

4. ADVANCED PLACEMENT PHYSICS B EQUATIONS
FLUID MECHANICS AND
THERMAL PHYSICS WAVES AND OPTICS
p p gh
F Vg
A A
p gy
T
Q mL
Q mc T
p
F
A
pV nRT
K k T
RT
M
k T
W p V
Q nc T
U Q W
U nc T
e
W
Q
e
T T
T
buoy
avg B
rms
B
V
H
c
H C
H
= +
=
=
+ + =
=
=
=
=
=
=
= =
= -
=
= +
=
=
=
-
0
1 1 2 2
2
0
1
2
3
2
3 3
r
r
u u
r ru
m
const.
D D
D
D
D
D
D D
l la
u
A = area
c = specific heat or molar
specific heat
e = efficiency
F = force
h = depth
Kavg = average molecular
kinetic energy
L = heat of transformation
l = length
M= molecular mass
m = mass of sample
n = number of moles
p = pressure
Q = heat transferred to a system
T = temperature
U = internal energy
V = volume
u = velocity or speed
urms = root-mean-square
velocity
W = work done on a system
y = height
a = coefficient of linear
expansion
µ = mass of molecule
r = density
u
u
q q
q
q l
l
=
=
=
=
+ =
= = -
=
=
f
n
c
n n
c
n
n
si s f
M
hi
h
si
s
f
R
d m
xm
m L
d
l
1 1 2 2
2
1
0
0 0
1 1 1
2
sin sin
sin
sin
Ϸ
d = separation
f = frequency or focal
length
h = height
L = distance
M= magnification
m = an integer
n = index of refraction
R = radius of curvature
s = distance
u = speed
x = position
l = wavelength
q = angle
ATOMIC AND NUCLEAR PHYSICS
E hf pc
K hf
h
p
E m c
= =
= −
=
=
max
( )
f
l
D D 2
E = energy
f = frequency
K = kinetic energy
m = mass
p = momentum
l = wavelength
f = work function
GEOMETRY AND TRIGONOMETRY
Rectangle
Triangle
Circle
Parallelepiped
Cylinder
Sphere
Right Triangle
A bh
A bh
A r
C r
V wh
V r
S r r
V r
S r
a b c
a
c
b
c
a
b
=
=
=
=
=
=
= +
=
=
+ =
=
=
=
1
2
2
2 2
4
3
4
2
2
2
3
2
2 2 2
p
p
p
p p
p
p
q
q
q
l
l
l
sin
cos
tan
A = area
C = circumference
V = volume
S = surface area
b = base
h = height
l = length
w = width
r = radius
c a
b
90q
x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 4

5. ADVANCED PLACEMENT PHYSICS C EQUATIONS
MECHANICS ELECTRICITY AND MAGNETISM
u u
u
u u
m
u
u w
u w
w
w w a
q q w a
= +
= + +
= + -
Ê = =
=
= I =
=
ˆ
= I
=
=
=
=
= =
= ™
Ê = =
= I = Ê
= ÊÊ
=
= ™ =
=
= +
= + +
= -
œ
0
0 0
0 0
0
0 0
1
2
2
1
2
1
2
1
2
2
2 2
2
2
2
2 2
2
2
at
x x t at
a x x
m
d
dt
dt
m
F N
W d
K m
P
dW
dt
P
U mgh
a
r
r
I
I r dm mr
m m
r
I
K I
t
t t
k
U
net
g
c
net
cm
s
fric
0 5
F F a
F
p
J F p
p v
F
r F
r r
L r p
F x
D
D
r
F vؒ
t
t t a
w
s
s
p
kx
T
f
T
m
k
T
g
Gm m
r
U
Gm m
r
G
G
=
= =
=
=
= -
= -
1
2
2 1
2
2
2
1 2
2
1 2
p
w
p
p l
F r$
a = acceleration
F = force
f = frequency
h = height
I = rotational inertia
J = impulse
K = kinetic energy
k = spring constant
l = length
L = angular momentum
m = mass
N = normal force
P = power
p = momentum
r = radius or distance
r = position vector
T = period
t = time
U = potential energy
u = velocity or speed
W = work done on a system
x = position
m = coefficient of friction
q = angle
t = torque
w = angular speed
a = angular acceleration
F
q q
r
q
d
Q
E
dV
dr
V
q
r
U qV
q q
r
C
Q
V
C
A
d
C C
C C
I
dQ
dt
U QV CV
R
A
V IR
R R
R R
P IV
q
d I
I d
B nI
d
d
dt
L
dI
i
ii
E
i
i
M
p i
i
s ii
c
s i
p i
s
m
m
=
=
=
= −
=
= =
=
=
=
=
=
= =
=
=
=
=
=
= ×
=
= I ×
=
= I
= −
= −
•
•
•
∑
∑
∑
∑
∑
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
2
p
p
p
k
r
m
m
f
f
e
e
⑀
⑀
⑀
⑀
⑀
E
F
E A
F v B
B
F B
B A
͛
͛
l
ø
ø
dt
U LIL =
1
2
2
A = area
B = magnetic field
C = capacitance
d = distance
E = electric field
e = emf
F = force
I = current
L = inductance
l = length
n = number of loops of wire per
unit length
P = power
Q = charge
q = point charge
R = resistance
r = distance
t = time
U = potential or stored energy
V = electric potential
u = velocity or speed
r = resistivity
fm = magnetic flux
k = dielectric constant
x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 5

6. ADVANCED PLACEMENT PHYSICS C EQUATIONS
GEOMETRY AND TRIGONOMETRY
Rectangle
Triangle
Circle
Parallelepiped
Cylinder
Sphere
Right Triangle
A bh
A bh
A r
C r
V wh
V r
S r r
V r
S r
a b c
a
c
b
c
a
b
=
=
=
=
=
=
= +
=
=
+ =
=
=
=
1
2
2
2 2
4
3
4
2
2
2
3
2
2 2 2
p
p
p
p p
p
p
l
l
l
sin
cos
tan
q
q
q
A = area
C = circumference
V = volume
S = surface area
b = base
h = height
l = length
w = width
r = radius
c a
b
90q
CALCULUS
df
dx
df
du
du
dx
d
dx
x nx
d
dx
e e
d
dx
x
x
d
dx
x x
d
dx
x x
x dx
n
x n
e dx e
dx
x
x
x dx x
x dx x
n n
x x
n n
x x
=
=
=
( ) =
( ) =
( ) = -
I =
+
ž -
I =
=
I =
I = -
-
+
I
2 7
2 7
1
1n
1n
1
1
1
1
1
sin cos
cos sin
,
cos sin
sin cos
x6-Physics Insert SINGLE PGS 3/21/01 3:24 AM Page 6