The AP Physics Equation Table

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Table
Exams
Table of
of Information
Information and
and Equation
Equation Tables
Tablesfor
forAP
AP® Physics
Physics Exams
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, A ) 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.
© 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, m p
1.67 – 10 27 kg
Neutron mass, mn
1.67 – 10 27 kg
Electron mass, me
9.11 – 10 31 kg
8.31 J (mol<K)
R
Universal gas constant,
1 electron volt, 1 eV
1.60 – 10 19 J
3.00 – 108 m s
c
6.67 – 10 11 m3 kg<s2
G
9.8 m s2
g
1.38 – 10 23 J K
Boltzmann’s constant, k B
1 unified atomic mass unit,
1u
1.66 – 10 27 kg
931 MeV c2
Planck’s constant,
h
6.63 – 10 34 J <s
4.14 – 10 15 eV <s
hc
1.99 – 10 25 J <m
1.24 – 10 3 eV < nm
�0
8.85 – 10 12 C2 N <m 2
Vacuum permittivity,
Coulomb’s law constant, k
Vacuum permeability,
Magnetic constant, k „
1 atmosphere pressure,
UNIT
SYMBOLS
1.60 – 10 19 C
Speed of light,
Universal gravitational
constant,
Acceleration due to gravity
at Earth’s surface,
6.02 – 1023 mol-1
Avogadro’s number, N 0
e
Electron charge magnitude,
meter,
kilogram,
second,
ampere,
kelvin,
PREFIXES
Factor
Prefix
Symbol
m
kg
s
A
K
mole,
hertz,
newton,
pascal,
joule,
1 4 p�0
9.0 – 109 N <m 2 C2
m0
4 p – 10 7 (T <m) A
m0 4 p
1 atm
mol
Hz
N
Pa
J
10 7 (T <m) A
1.0 – 105 N m2
watt,
coulomb,
volt,
ohm,
henry,
W
C
V
W
H
1.0 – 105 Pa
farad,
tesla,
degree Celsius,
electron-volt,
F
T
’C
eV
VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
D
q
30D
0
37D
45D
53D
60D
90D
109
giga
G
sin q
0
12
35
2 2
4 5
3 2
1
106
mega
M
cosq
1
3 2
4 5
2 2
35
12
0
103
kilo
k
tanq
0
3 3
3 4
1
43
3
‡
2
centi
c
10 3
milli
m
10 6
micro
m
9
nano
n
12
pico
p
10
10
10
The following conventions are used in this exam.
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.
© 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
u
u0 at
x
x0 u0 t u2
u02 2a x x0 ÇF
ma
Fnet
F fric … m N
ac
u2
r
t
r F sin q
p
mv
J
K
FDt
mgh
F Dr cos q
W
Dt
Pavg
P
Dp
1 2
mu
2
DUg
W
1 2
at
2
F u cos q
Fs
k x
Us
1 2
kx
2
m
k
Ts
2p
Tp
A
2p
g
T
1
f
Gm1m2
FG
UG
Gm1m2
r
r2
a
F
f
h
J
K
k
A
m
N
P
p
r
T
t
U
u
W
x
m
q
t
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
acceleration
force
frequency
height
impulse
kinetic energy
spring constant
length
mass
normal force
power
momentum
radius or distance
period
time
potential energy
velocity or speed
work done on a system
position
coefficient of friction
angle
torque
ELECTRICITY AND MAGNETISM
F
1 q1q2
4 p�0 r 2
E
F
q
UE
Eavg
V
C
C
Uc
1 q1q2
4 p�0 r
qV
V
d
q
1
4 p�0
Ç rii
i
Q
V
�0 A
d
1
QV
2
1
CV 2
2
DQ
Dt
I avg
R
rA
A
V
IR
P
IV
Cp
Ç Ci
1
Cs
ÇC
Rs
Ç Ri
1
Rp
ÇR
FB
qu B sin q
FB
BI A sin q
B
fm
i
1
i
1
i
i
m0 I
2p r
BA cos q
eavg
e
i
i
B Au
© 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and
www.collegeboard.com/apstudents (for students and parents).
Dfm
Dt
A
B
C
d
E
e
F
I
A
P
Q
q
R
r
t
U
V
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
u =
r =
q =
fm =
area
magnetic field
capacitance
distance
electric field
emf
force
current
length
power
charge
point charge
resistance
distance
time
potential (stored) energy
electric potential or
potential difference
velocity or speed
resistivity
angle
magnetic flux
ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2008 and 2009
FLUID MECHANICS AND THERMAL PHYSICS
WAVES AND OPTICS
P
u
fl
n
c
u
P0 r gh
Fbuoy
rVg
A1u1
A2 u2
1
P r gy ru 2
2
DA
a A 0 DT
H
kA DT
L
P
F
A
PV
nRT
Nk BT
K avg
3
k T
2 B
urms
3 RT
M
W
PDV
DU
const.
Q W
e
W
QH
ec
TH TC
TH
3k BT
m
A = area
e = efficiency
F = force
h = depth
H = rate of heat transfer
k = thermal conductivity
Kavg = average molecular
kinetic energy
A = length
L = thickness
M = molar mass
n = number of moles
N = number of molecules
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
m = mass of molecule
r = density
ATOMIC AND NUCLEAR PHYSICS
E
hf
K max
l
DE
pc
hf f
h
p
( Dm ) c 2
E=
f =
K=
m=
p =
l=
f=
energy
frequency
kinetic energy
mass
momentum
wavelength
work function
n 1 sin q1
n 2 sin q2
n2
n1
sin qc
1
1
si s0
M
1
f
hi
h0
R
2
d sin q
s
i
s0
f
xm 
ml
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
m lL
d
GEOMETRY AND TRIGONOMETRY
Rectangle
A bh
Triangle
1
A
bh
2
Circle
A pr2
C 2p r
Parallelepiped
V Awh
Cylinder
V p r 2A
A=
C=
V=
S =
b =
h =
A=
w=
r =
area
circumference
volume
surface area
base
height
length
width
radius
S 2p r A 2p r 2
Sphere
4 3
pr
V
3
S 4p r 2
Right Triangle
a 2 b2 c 2
a
sin q
c
b
cos q
c
a
tan q
b
c
q
a
90q
b
© 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
u
u0 at
x
x0 u0 t u2
ÇF
1 2
at
2
u0 2 2a x x0 ma
Fnet
F
dp
dt
J
Ô F dt
p
mv
Dp
F fric … m N
W
Ô F<dr
K
1 2
mu
2
P
dW
dt
P
F<v
DUg
ac
t
Çt
I
rcm
mgh
2
u
r
t net
Ô r dm
2
L
r–p
K
1 2
Iw
2
q
F
1 q1q2
4 p�0 r 2
E
F
q
Ia
Ç mr
w0 at
q0 w0t 1 2
at
2
dV
dr
V
1
4 p�0
UE
q
Ç rii
i
1 q1q2
4 p�0 r
qV
C
Q
V
C
k �0 A
d
Cp
Ç Ci
1
Cs
ÇC
I
i
1
i
i
dQ
dt
k x
Uc
1
QV
2
Us
1 2
kx
2
R
rA
A
E
rJ
I
Neud A
V
IR
2
Iw
�0
E
T
2p
w
1
f
m
k
Ts
2p
Tp
A
2p
g
Gm1m2
FG
UG
Gm1m2
r
r2
Rs
rˆ
1
Rp
P
FM
Ç Ri
A
B
C
d
E
e
Q
vÔ E < d A
Fs
Ç mr Ç m
rw
acceleration
force
frequency
height
rotational inertia
impulse
kinetic energy
spring constant
length
angular momentum
mass
normal force
power
momentum
radius or distance
position vector
period
time
potential energy
velocity or speed
work done on a system
position
coefficient of friction
angle
torque
angular speed
angular acceleration
w2 r
r–F
u
w
a =
F =
f =
h =
I =
J =
K =
k =
A =
L =
m=
N =
P =
p =
r =
r =
T =
t =
U=
u =
W=
x =
m=
q =
t =
w =
a =
ELECTRICITY AND MAGNETISM
1
CV 2
2
F
I
J
L
A
n
=
=
=
=
=
=
=
=
=
=
=
=
N =
=
=
=
=
=
=
=
V=
u =
r =
fm =
k =
P
Q
q
R
r
t
U
vÔ B< d �
F
IV
qv – B
© 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and
www.collegeboard.com/apstudents (for students and parents).
m0 I
m0 I d � – r
4p r3
dB
Ô I d� – B
Bs
m0 nI
fm
Ô B<dA
i
1
ÇR
i
i
area
magnetic field
capacitance
distance
electric field
emf
force
current
current density
inductance
length
number of loops of wire
per unit length
number of charge carriers
per unit volume
power
charge
point charge
resistance
distance
time
potential or stored energy
electric potential
velocity or speed
resistivity
magnetic flux
dielectric constant
d fm
dt
e
e
L
UL
dI
dt
1 2
LI
2
ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2008 and 2009
GEOMETRY AND TRIGONOMETRY
Rectangle
A bh
Triangle
1
bh
2
A
Circle
pr2
A
C 2p r
Parallelepiped
V Awh
Cylinder
V
p r 2A
S
2p r A 2p r 2
A=
C=
V=
S =
b =
h =
A =
w=
r =
CALCULUS
df
dx
area
circumference
volume
surface area
base
height
length
width
radius
Sphere
d f du
du dx
d n
x dx
nx n 1
d x
e dx
ex
d
1n x dx
1
x
d
sin x dx
cos x
d
cos x dx
sin x
Ôx
n
dx
1
x n 1 , n › 1
n 1
Ôe
x
dx
ex
dx
x
V
4 3
pr
3
Ô
S
4p r 2
Ô cos x dx
sin x
Ô sin x dx
cos x
Right Triangle
a2 b2
c2
sin q
a
c
cos q
b
c
tan q
a
b
c
q
ln x
a
90q
b
© 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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