Table of Information and Equation Tables for AP 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 examination 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.
TABLE OF INFORMATION FOR 2006 and 2007
CONSTANTS AND CONVERSION FACTORS UNITS PREFIXES
1 unified atomic mass unit, 1 u = 1.66 ¥ 10 -27 kg Name Symbol Factor Prefix Symbol
9
= 931 MeV c 2 10 giga G
meter m
6
Proton mass, m p = 1.67 ¥ 10 -27 kg kilogram kg
10 mega M
3
Neutron mass, mn = 1.67 ¥ 10 -27 kg 10 kilo k
second s -2
Electron mass, me = 9.11 ¥ 10 -31 kg 10 centi c
ampere A -3
Electron charge magnitude, e = 1.60 ¥ 10 -19 C 10 milli m
-6
Avogadro’s number, N 0 = 6.02 ¥ 1023 mol -1 kelvin K 10 micro m
Universal gas constant, R = 8.31 J (moliK) mole mol 10 -9 nano n
Boltzmann’s constant, k B = 1.38 ¥ 10 -23
J K -12
hertz Hz 10 pico p
Speed of light, c = 3.00 ¥ 10 m s 8
newton N
-34
Planck’s constant, h = 6.63 ¥ 10 J is pascal Pa VALUES OF
-15 TRIGONOMETRIC
= 4.14 ¥ 10 eV is FUNCTIONS FOR COMMON
joule J
hc = 1.99 ¥ 10 -25 J im ANGLES
watt W
= 1.24 ¥ 103 eV inm θ sin θ cos θ tan θ
Vacuum permittivity, 0 = 8.85 ¥ 10 -12 C2 N im 2 coulomb C
0 0 1 0
Coulomb’s law constant, k = 1 4p = 9.0 ¥ 10 9 N im 2 C2 volt V
0
Vacuum permeability, m0 = 4 p ¥ 10 -7 (T im) A ohm W 30 1/2 3 /2 3 /3
Magnetic constant, k ¢ = m0 4 p = 10 -7 (T im) A henry H
37 3/5 4/5 3/4
Universal gravitational constant, G = 6.67 ¥ 10 -11 m 3 kgis2 farad F
Acceleration due to gravity tesla T 45 2 /2 2 /2 1
at Earth’s surface, g = 9.8 m s2 degree
53 4/5 3/5 4/3
1 atmosphere pressure, 1 atm = 1.0 ¥ 10 N m 5 2
Celsius C
= 1.0 ¥ 105 Pa electron- 60 3 /2 1/2 3
1 electron volt, 1 eV = 1.60 ¥ 10 -19 J volt eV
90 1 0 ∞
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.
ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2006 and 2007
NEWTONIAN MECHANICS ELECTRICITY AND MAGNETISM
u = u0 + at a = acceleration 1 q1q2 A = area
F =
F = force 4p 0 r 2 B = magnetic field
1 2
x = x0 + u0 t + at f = frequency
F
C = capacitance
2 h = height E= d = distance
q
J = impulse E = electric field
u 2 = u0 2 + 2a ( x - x0 )
K = kinetic energy UE = qV =
1 q1q2 e = emf
4p 0 r
 F = Fnet = ma k = spring constant F = force
= length V I = current
F fric £ m N m = mass Eavg = - = length
d
N = normal force P = power
 rii
1 q
u2 P = power V = Q = charge
ac = 4p 0
r p = momentum i q = point charge
t = r F sin q r = radius or distance Q R = resistance
C =
T = period V r = distance
p = mv t = time t = time
0A
U = potential energy C = U = potential (stored) energy
J = FDt = Dp d
u = velocity or speed V = electric potential or
1 1
1 2 W = work done on a system Uc = QV = CV 2 potential difference
K = mu 2 2
2 x = position u = velocity or speed
m = coefficient of friction DQ r = resistivity
DUg = mgh I avg =
q = angle Dt q = angle
W = F Dr cos q t = torque r fm = magnetic flux
R=
A
Pavg =
W V = IR
Dt
P = IV
P = F u cos q Cp = Â Ci
i
Fs = - k x
1 1
=Â
1 2 Cs i Ci
Us = kx
2
Rs = Â Ri
i
m
Ts = 2 p
1 1
k
Rp
= ÂR
i i
Tp = 2p
g FB = qu B sin q
1 FB = BI sin q
T =
f m0 I
B=
Gm1m2 2p r
FG = -
r2 fm = BA cos q
Dfm
UG = -
Gm1m2 eavg =-
r Dt
e = B u
ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2006 and 2007
FLUID MECHANICS AND THERMAL PHYSICS WAVES AND OPTICS
P = P0 + r gh A = area u = fl d = separation
e = efficiency f = frequency or
c
Fbuoy = rVg F = force n= focal length
u
h = depth h = height
A1u1 = A2 u2 H = rate of heat transfer n 1 sin q1 = n 2 sin q2 L = distance
k = thermal conductivity n2 M = magnification
1 2 sin qc =
P + r gy + ru = const. Kavg = average molecular n1 m = an integer
2 kinetic energy n = index of
1 1 1
D =a = length + = refraction
0 DT si s0 f
L = thickness R = radius of
kA DT M = molar mass curvature
h s
H = n = number of moles M = i =- i s = distance
L h0 s0
N = number of molecules u = speed
F R x = position
P= P = pressure f =
A Q = heat transferred to a 2 l = wavelength
system d sin q = ml q = angle
PV = nRT = Nk BT
T = temperature
m lL
3 U = internal energy xm
K avg = k BT V = volume
d
2
3k B T u = velocity or speed GEOMETRY AND TRIGONOMETRY
3 RT
urms = = urms = root-mean-square
M m Rectangle A= area
velocity
A = bh C= circumference
W = - P DV W = work done on a system Triangle V= volume
y = height
DU = Q + W 1
A = bh S = surface area
a = coefficient of linear 2
expansion b = base
W Circle h = height
e= m = mass of molecule
QH A = pr2 = length
r = density C = 2p r w= width
TH - TC Parallelepiped r = radius
ec =
TH V = wh
Cylinder
V = pr2
ATOMIC AND NUCLEAR PHYSICS S = 2p r + 2p r 2
E = hf = pc E= energy Sphere
f = frequency 4
K max = hf - f V = pr3
K= kinetic energy 3
h m= mass S = 4p r 2
l = p = momentum Right Triangle
p
l= wavelength a 2 + b2 = c 2
D E = ( Dm ) c 2 f= work function
a
sin q = c
c a
b q 90°
cos q =
c b
a
tan q =
b
ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2006 and 2007
MECHANICS ELECTRICITY AND MAGNETISM
u = u0 + at a = acceleration 1 q1q2 A = area
F =
F = force 4p 0 r 2 B = magnetic field
1 2
x = x0 + u0 t + at f = frequency C = capacitance
2 F
h = height E= d = distance
q
I = rotational inertia E = electric field
u 2 = u02 + 2a ( x - x0 )
J = impulse Q e = emf
 F = Fnet = ma K = kinetic energy ÚE ∑ dA=
0
F = force
k = spring constant I = current
dp = length dV J = current density
F= E =-
dt L = angular momentum dr L = inductance
m= mass = length
J = Ú F dt = Dp
q
N = normal force V =
1
4p 0 Â rii n = number of loops of wire
P = power i per unit length
p = mv N = number of charge carriers
p = momentum 1 q1q2
r = radius or distance UE = qV = per unit volume
F fric £ m N 4p 0 r
r = position vector P = power
Q Q = charge
ÚF
W = ∑ dr T = period C =
t = time V q = point charge
U= potential energy R = resistance
1 2 k 0A
K = mu u = velocity or speed C = r = distance
2 d
W= work done on a system t = time
P=
dW x = position Cp = Â Ci U = potential or stored energy
dt i V= electric potential
m = coefficient of friction
q = 1 1 u = velocity or speed
P=F v angle =Â
t = torque Cs i Ci
r = resistivity
DUg = mgh w = angular speed fm = magnetic flux
dQ
a = angular acceleration I = k = dielectric constant
u 2 dt
ac = = w2 r
r 1 1
Fs = - k x Uc = QV = CV 2
t=r¥F
2 2 ÚB ∑ d = m0 I
1 2 r m0 I d ¥ r
 t = t net = I a Us = kx R=
2 A dB =
4p r 3
I = Ú r 2 dm = Â mr 2 2p 1 E = rJ
T =
w
=
f
I = Neud A
F= ÚI d ¥B
rcm =  mr  m
m Bs = m0 nI
u = rw Ts = 2 p V = IR
k
fm = Ú B ∑ d A
L = r ¥ p = Iw
Rs = Â Ri
i
Tp = 2 p d fm
g e =-
1 1 1
K = I w2
2 Rp
= ÂR dt
Gm1m2 i i
FG = - ˆ
r dI
w = w0 + at r2 e = -L
P = IV dt
Gm1m2 1 2
1 2 UG =- FM = qv ¥ B UL = LI
q = q0 + w0t + at r 2
2
ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2006 and 2007
GEOMETRY AND TRIGONOMETRY CALCULUS
Rectangle A= area df d f du
=
A = bh C= circumference dx du dx
V= volume
Triangle
S = surface area
d n
dx
( x ) = nxn -1
1
A= bh b = base
Circle
2 h = height d x
dx
(e ) = e x
= length
A = pr2 w= width d
(1n x ) = 1
r = radius dx x
C = 2p r
d
Parallelepiped (sin x ) = cos x
dx
V = wh
d
Cylinder (cos x ) = - sin x
dx
V = pr2 1
Úx dx = x n + 1 , n π -1
n
n +1
S = 2p r + 2p r 2
Úe dx = e x
x
Sphere
4 3
Ú
V = dx
pr = ln x
3 x
S = 4p r 2
Ú cos x dx = sin x
Right Triangle
a 2 + b2 = c 2 Ú sin x dx = - cos x
a c
sin q = a
c
q 90°
b b
cos q =
c
a
tan q =
b