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ap physics b/c equation sheet
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Content Preview
Tab
ab le of Infor
r ma
a ttiio
o n
n and Equattion T
T ab
abl le
e s
s ffo
o r
r A
A P
P (R) Ph
P y
h si
s c
i s
c
s E
x
E a
x m
a s
m s

The accompanying Table of Information and Equation Tables will be provided to students when
they take the AP Physics Exams. Therefore, students may NOT bring their own copies of these
tables to the exam room, although they may use them throughout the year in their classes in
order to become familiar with their content.

Table of Information
For both the Physics B and Physics C Exams, the Table of Information is printed near the front
cover of the multiple-choice section and on the green insert provided with the free-response
section. The tables are identical for both exams except for one convention as noted.

Equation Tables
For both the Physics B and Physics C Exams, the equation tables for each exam are printed only
on the green insert provided with the free-response section. The equation tables may be used by
students when taking the free-response sections of both exams but NOT when taking the
multiple-choice sections.
The equations in the tables express the relationships that are encountered most frequently in
AP Physics courses and exams. However, the tables do not include all equations that might
possibly be used. For example, they do not include many equations that can be derived by
combining other equations in the tables. Nor do they include equations that are simply special
cases of any that are in the tables. Students are responsible for understanding the physical
principles that underlie each equation and for knowing the conditions for which each equation is
applicable.
The equation tables are grouped in sections according to the major content category in which
they appear. Within each section, the symbols used for the variables in that section are defined.
However, in some cases the same symbol is used to represent different quantities in different
tables. It should be noted that there is no uniform convention among textbooks for the symbols
used in writing equations. The equation tables follow many common conventions, but in some
cases consistency was sacrificed for the sake of clarity.
Some explanations about notation used in the equation tables:
1. The symbols used for physical constants are the same as those in the Table of
Information and are defined in the Table of Information rather than in the right-hand
columns of the tables.
2. Symbols in bold face represent vector quantities.
3. Subscripts on symbols in the equations are used to represent special cases of the
variables defined in the right-hand columns.
4. The symbol D before a variable in an equation specifically indicates a change in the
variable (i.e., final value minus initial value).
5. Several different symbols (e.g., d, r, s, h, ) are used for linear dimensions such as
length. The particular symbol used in an equation is one that is commonly used for
that equation in textbooks.
(c) 2007 The College Board. All rights reserved. College Board, Advanced Placement Program, AP, and the acorn logo are registered
trademarks of the College Board.



TABLE OF INFORMATION FOR 2008 and 2009
CONSTANTS AND CONVERSION FACTORS
Proton mass,
27
m
1.67 10
kg
p
Electron charge magnitude,
19
e
1.60 10
C
Neutron mass,
27
1.67 10
kg
19
n
m

1 electron volt, 1 eV
1.60 10
J
Electron mass,
31
9.11 10
kg
e
m

Speed of light,
8
c
3.00 10 m s
Avogadro's number,
23
-1
Universal gravitational
N
11
3
2
0
6.02 10 mol
constant,
G
6.67 10
m kg s
Universal gas constant,
R
8.31 J (mol K)
Acceleration due to gravity
2
at Earth's surface,
g
9.8 m s
Boltzmann's constant,
23
k
1.38 10
J K
B



1 unified atomic mass unit,
27
2
1 u
1.66 10
kg
931 MeV c
Planck's constant,
34
15
h
6.63 10
J s
4.14 10
eV s
25
3
hc
1.99 10
J m
1.24 10 eV nm
Vacuum permittivity,
12
2
2
0
8.85 10
C N m
Coulomb's law constant,
9
2
k
1 4p
2
0
9.0 10 N m C
Vacuum permeability,
7
0
m
4p
10 (T m) A
Magnetic constant,
7
k
0
m 4p
10 (T m) A
1 atmosphere pressure,
5
2
5
1 atm
1.0 10 N m
1.0 10 Pa

meter,
m
mole,
mol
watt,
W
farad,
F
kilogram,
kg
hertz,
Hz
coulomb,
C
tesla,
T
UNIT
second,
s
newton,
N
volt,
V
degree Celsius,
C
SYMBOLS
ampere,
A
pascal,
Pa
ohm,
W
electron-volt,
eV
kelvin,
K
joule,
J
henry,
H





PREFIXES
VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
Factor
Prefix
Symbol

q
0
30
37
45
53
60
90
9
10
giga
G

sinq
0
1 2
3 5
2 2
4 5
3 2
1
6

cosq
1
3 2
4 5
10
mega
M
2 2
3 5
1 2
0
3
10
kilo
k

tanq
0
3 3
3 4
1
4 3
3

2
10

centi
c

The following conventions are used in this exam.
3
10

milli
m
I. Unless otherwise stated, the frame of reference of any problem is
6
10

micro
m


assumed to be inertial.
9
II. The direction of any electric current is the direction of flow of positive
10

nano
n
charge (conventional current).
12
10

pico
p
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.


(c) 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and
www.collegeboard.com/apstudents (for students and parents).

ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2008 and 2009
NEWTONIAN MECHANICS
ELECTRICITY AND MAGNETISM
u
q q
0
u
at
a = acceleration
1
1 2
F
A = area
F = force
2
4p0 r
B = magnetic field
1 2
x
f = frequency
C = capacitance
0
x
0
u t
at
2
F
h = height
E
q
d = distance
2
2
J = impulse
E = electric field
u
0
u
2a x
0
x
K = kinetic energy
1
1
q 2
q
e = emf
E
U
qV
F
k = spring constant
4p
r
F = force
n
F et
ma
0
= length
V
I = current
F
E
fric
mN
m = mass
avg
d
= length
N = normal force
P = power
2
q
u
P = power
1
i
V
Q = charge
c
a
r
4p
r
p = momentum
0 i
i
q = point charge
t
rF sin q
r = radius or distance
Q
C
R = resistance
T = period
V
r = distance
p
mv
t = time

t = time
0 A
C
J
U = potential energy
D
F t
Dp
d
U = potential (stored) energy
u = velocity or speed
V = electric potential or
1
1
1
2
2
K
m
W = work done on a system
potential difference
u
c
U
QV
CV
2
2
2
x = position
u = velocity or speed
m = coefficient of friction
DQ
r = resistivity
D
I
g
U
mgh
avg
q = angle
Dt
q = angle
W
FDr cos q
t = torque
R
r
fm = magnetic flux
A
W
V
IR
a
P vg
t
D
P
IV
P
Fu cosq
Cp
i
C
i
s
F
kx
1
1
1
C
C
2
U
s
i
i
s
kx
2
s
R
i
R
m
i
T
2
s
p k
1
1
Rp
i
i
R
T
2
p
p g
u sin
B
F
q B
q
1
sin
T
B
F
BI
q
f
0
m I
B
G
2p r
1
m 2
m
G
F
2
r
f
cos
m
BA
q
G
m
f
1
m 2
m
e
D
G
U
avg
r
Dt
e
B u
(c) 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and
www.collegeboard.com/apstudents (for students and parents).

ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2008 and 2009
FLUID MECHANICS AND THERMAL PHYSICS
WAVES AND OPTICS
P
A = area
u
f l
d = separation
0
P
rgh
e = efficiency
c
f = frequency or
n
b
F uoy
Vg
r

F = force

focal length
u
h = depth
h = height
n sin q
n sin
1
A 1
u
2
A 2
u
H = rate of heat transfer
1
1
2
2
q
L = distance
k = thermal conductivity
n
M = magnification
1
2
2
P
sinq

rgy
ru
const.
K
c
n
m = an integer
2
avg = average molecular
1

kinetic energy
n = index of
1
1
1
D
a
= length


refraction
0 T
D
L = thickness
s
0
s
f
i
R = radius of
kADT
M = molar mass

curvature
H
h
s
i
i
L
n = number of moles
M
s = distance
h
s
N = number of molecules
0
0
u = speed
F
P
P = pressure
R
x = position
A
f

Q = heat transferred to a
2
l = wavelength
PV
nRT
Nk
system
d sinq
ml
q = angle
BT
T = temperature
mlL
3
U = internal energy
x
K
m
d
avg
k T
2 B
V = volume
3RT
3k
u = velocity or speed
BT
GEOMETRY AND TRIGONOMETRY
r
u ms
M

m
urms = root-mean-square
Rectangle

velocity
A = area
A
bh
W
P
C = circumference
DV
W = work done on a system
Triangle
V = volume
y = height
DU
Q W
1
a = coefficient of linear
A
b
S = surface area
h
2
b = base
W
expansion
e
Circle
m = mass of molecule
h = height
2
H
Q
A
pr
= length
r = density
C
2pr
w = width
H
T
C
T

Parallelepiped
r = radius
c
e
H
T

V
h
w

Cylinder


V
p 2

r
ATOMIC AND NUCLEAR PHYSICS

p
pr

S
r
2
2
2


E
hf
pc
E = energy
Sphere

f = frequency
4
3

K

V
pr
max
hf
f
K = kinetic energy
3


h
m = mass

S
r2
4p
l

p
p = momentum

Right Triangle

l = wavelength

2
2
2
a
b
c

2

DE
(Dm)c
f = work function
a

sin q


c

c
a

cos
b
q

q
90
c

b


a
ta

n q

b



(c) 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and
www.collegeboard.com/apstudents (for students and parents).

ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2008 and 2009
MECHANICS
ELECTRICITY AND MAGNETISM
u
q q
0
u
at
a = acceleration
1
1 2
F
A = area
F = force
2
4p0 r
B = magnetic field
1 2
x
f = frequency
C = capacitance
0
x
0
u t
at
2
h = height
F
E
d = distance
q
2
2
I = rotational inertia
E = electric field
u
0
u
2a x
0
x
J = impulse
Q
e = emf
E dA
F
K = kinetic energy
F = force
n
F et
ma
0
k = spring constant
I = current
dp
dV
F
= length
E
J = current density
dt
L = angular momentum
dr
L = inductance
m = mass
= length
J
F dt
Dp
1
q
N = normal force
i
V
4p
r
n = number of loops of wire
P = power
0 i
i
per unit length
p
mv
p = momentum
1
N = number of charge carriers
1
q 2
q
U
qV
F
r = radius or distance
E
per unit volume
fric
mN
4p0 r
r = position vector
P = power
Q = charge
W
F dr
T = period
Q
C
t = time
V
q = point charge
R = resistance
1
U = potential energy
2
K
mu
k0 A
r = distance
2
u = velocity or speed
C
d
W = work done on a system
t = time
dW
P
x = position
Cp
i
C
U = potential or stored energy
dt
m = coefficient of friction
i
V = electric potential
P
F v
q = angle
1
1
u = velocity or speed
t = torque
Cs
i
i
C
r = resistivity
D g
U
mgh
w = angular speed
f
dQ
m = magnetic flux
a = angular acceleration
I
k = dielectric constant
2
u
dt
2
c
a
w r
r
1
1
2
F
x
c
U
QV
CV
t
r
F
s
k
2
2
B d
0
m I
t
t
1
r
net
Ia
2
s
U
kx
R
0
m I d
r
2
A
dB

p
r3
4
2
2
I
r dm
mr
2p
1
E
rJ
T
w
f
F
I d B
I
Neu A
c
r m
mr m
d
m
s
B
0
m nI
u
rw
T
2
s
p k
V
IR
f
B A
L
r
p
I
m
d
w
R
R
s
i
T
2
i
p
p g
df
1
m
2
K
I
e
w
1
1
dt
2
G
R
R
1
m 2
m
F

i
p
i
G
r
dI
w
2
r
e
L
0
w
at
P
IV
dt
1
Gm m
1
2
1 2
2
q
U
F
v
B
U
LI
0
q
0
w t
at
G
M
q
2
r
L
2
(c) 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and
www.collegeboard.com/apstudents (for students and parents).

ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2008 and 2009


GEOMETRY AND TRIGONOMETRY
CALCULUS

Rectangle
A = area
d f
d f du
A
bh
C = circumference
dx
du dx
Triangle
V = volume
d
n
n 1
S = surface area
x
nx
dx


1
A
bh
b = base
2
h = height
d x
x
e
e
Circle
= length
dx


d

2
A
1
pr
w = width
1n x
r = radius
dx
x
C
2pr

d
Parallelepiped

sin x
cos x
dx

V
wh


d
x
x
Cylinder
cos
sin

dx


2
V
pr


n
1
n 1

x dx
x
, n
1
n

1
S
pr
pr2
2
2


x
x
e dx
e
Sphere


dx

4
3
V

pr
ln x
3

x



2
S
4pr

cos x dx
sin x
Right Triangle


sin x dx
cos x
2
2
a
b
c2


a
sin q
c
a
c
q
90
cos
b
q

b

c

a
tan q

b


(c) 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and
www.collegeboard.com/apstudents (for students and parents).

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