ADVANCED PLACEMENT PHYSICS 2 EQUATIONS, EFFECTIVE 2015
CONSTANTS AND CONVERSION FACTORS
Proton mass, m p = 1.67 ¥ 10 -27 kg
Neutron mass, mn = 1.67 ¥ 10 -27 kg
1 electron volt, 1 eV = 1.60 ¥ 10 -19 J
Electron mass, me = 9.11 ¥ 10 -31 kg
c = 3.00 ¥ 108 m s
Speed of light,
Universal gravitational
constant,
Acceleration due to gravity
at Earth’s surface,
Avogadro’s number, N 0 = 6.02 ¥ 10 23 mol-1
R = 8.31 J (moliK)
Universal gas constant,
e = 1.60 ¥ 10 -19 C
Electron charge magnitude,
G = 6.67 ¥ 10 -11 m 3 kg is 2
g = 9.8 m s 2
Boltzmann’s constant, k B = 1.38 ¥ 10 -23 J K
1 u = 1.66 ¥ 10 -27 kg = 931 MeV c 2
1 unified atomic mass unit,
h = 6.63 ¥ 10 -34 Jis = 4.14 ¥ 10 -15 eVis
Planck’s constant,
hc = 1.99 ¥ 10 -25 Ji m = 1.24 ¥ 103 eVinm
e0 = 8.85 ¥ 10 -12 C2 N i m 2
Vacuum permittivity,
Coulomb’s law constant, k = 1 4 pe0 = 9.0 ¥ 10 9 N i m 2 C2
m0 = 4 p ¥ 10 -7 (Ti m) A
Vacuum permeability,
Magnetic constant, k ¢ = m0 4 p = 1 ¥ 10 -7 (T i m) A
1 atm = 1.0 ¥ 10 5 N m 2 = 1.0 ¥ 10 5 Pa
1 atmosphere pressure,
UNIT
SYMBOLS
Factor
1012
meter,
kilogram,
second,
ampere,
kelvin,
PREFIXES
Prefix
Symbol
tera
T
m
kg
s
A
K
mole,
hertz,
newton,
pascal,
joule,
mol
Hz
N
Pa
J
watt,
coulomb,
volt,
ohm,
henry,
farad,
tesla,
degree Celsius,
electron volt,
W
C
V
W
H
F
T
∞C
eV
VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
q
0
30
37
45
53
60
sin q
0
12
35
2 2
45
3 2
1
90
10 9
giga
G
106
mega
M
cosq
1
3 2
45
2 2
35
12
0
10 3
kilo
k
tan q
0
33
34
1
43
3
•
10 -2
centi
c
10 -3
milli
m
10 -6
micro
m
-9
nano
n
10 -12
pico
p
10
The following conventions are used in this exam.
I. The frame of reference of any problem is assumed to be inertial unless
otherwise stated.
II. In all situations, positive work is defined as work done on a system.
III. The direction of current is conventional current: the direction in which
positive charge would drift.
IV. Assume all batteries and meters are ideal unless otherwise stated.
V. Assume edge effects for the electric field of a parallel plate capacitor
unless otherwise stated.
VI. For any isolated electrically charged object, the electric potential is
defined as zero at infinite distance from the charged object.
ADVANCED PLACEMENT PHYSICS 2 EQUATIONS, EFFECTIVE 2015
MECHANICS
Ãx = Ãx 0 + a x t
x = x 0 + Ãx 0 t +
1 2
a t
2 x
Ãx2 = Ãx20 + 2ax ( x - x0 )


Fnet
 ÂF
a =
=
m
m


Ff £ m Fn
Ã2
r


p = mv
ac =


Dp = F Dt
K =
1 2
mv
2
DE = W = Fd = Fd cos q
P =
DE
Dt
q = q0 + w0 t +
1 2
at
2
w = w0 + at
x = A cos ( wt ) = A cos (2 p ft )
xcm =
 mi xi
 mi


t net
 Ât
a=
=
I
I
t = r^ F = rF sin q
L = Iw
DL = t Dt
1
K = I w2
2


Fs = k x
a =
A =
d =
E =
F =
f =
I =
K =
k =
L =
 =
m =
P =
p =
r =
T =
t =
U =
v =
W=
x =
y =
a =
m=
q =
t =
w=
ELECTRICITY AND MAGNETISM
acceleration
amplitude
distance
energy
force
frequency
rotational inertia
kinetic energy
spring constant
angular momentum
length
mass
power
momentum
radius or separation
period
time
potential energy
speed
work done on a system
position
height
angular acceleration
coefficient of friction
angle
torque
angular speed
Us =
1 2
kx
2
DUg = mg Dy
T =
2p
1
=
w
f

FE =
1 q1q2
4 pe0 r 2


FE
E =
q

E =
1 q
4 pe0 r 2
DU E = qDV
1 q
4 pe0 r
V =

DV
E =
Dr
DV =
Q
C
C = ke0
A
d
Q
e0 A
E =
UC =
1
1
QDV = C ( DV )2
2
2
I =
DQ
Dt
R=
r
A
P = I DV
I =
DV
R
=
=
=
=
=
e=
F =
I =
 =
P =
Q =
q =
R =
r =
t =
U =
V =
v =
k =
r=
q =
F=
area
magnetic field
capacitance
distance
electric field
emf
force
current
length
power
charge
point charge
resistance
separation
time
potential (stored)
energy
electric potential
speed
dielectric constant
resistivity
angle
flux

 
FM = qv ¥ B



FM = qv sin q B
 

FM = I  ¥ B
i



FM = I  sin q B
 
F B = B A
 Ri
Rs =
A
B
C
d
E
m
k
1
=
Rp
 R1i

Tp = 2 p
g
Cp =
 Ci


FB = B cos q A

mm
Fg = G 1 2 2
r

 Fg
g=
m
1
=
Cs
 C1i
B
e = - DF
Dt
Ts = 2 p
UG = -
Gm1m2
r
B=
i
i
i
m0 I
2p r
e=
B v
ADVANCED PLACEMENT PHYSICS 2 EQUATIONS, EFFECTIVE 2015
FLUID MECHANICS AND THERMAL PHYSICS
r=
m
V
P=
F
A
A
F
h
k
K
L
m
n
N
P
Q
P = P0 + rgh
Fb = rVg
A1v1 = A2 v2
P1 + rgy1 +
1
rv 2
2 1
= P2 + rgy2 +
kA DT
Q
=
Dt
L
PV = nRT = NkBT
K =
1
rv 2
2 2
= area
= force
= depth
= thermal conductivity
= kinetic energy
= thickness
= mass
= number of moles
= number of molecules
= pressure
= energy transferred to a
system by heating
T = temperature
t = time
U = internal energy
V = volume
v = speed
W = work done on a system
y = height
r = density
3
k T
2 B
MODERN PHYSICS
h
l=
p
E = mc
2
v
f
n=
c
Ã
n 1 sin q1 = n 2 sin q2
1
1
1
+
=
si so
f
M =
hi
s
= i
ho
so
DL = m l
d sin q = m l
E=
f =
K=
m=
p =
l=
f=
energy
frequency
kinetic energy
mass
momentum
wavelength
work function
d = separation
f = frequency or
focal length
h = height
L = distance
M = magnification
m = an integer
n = index of
refraction
s = distance
v = speed
l = wavelength
q = angle
GEOMETRY AND TRIGONOMETRY
Rectangle
A = bh
Circle
DU = Q + W
K max = hf - f
l=
Triangle
1
A = bh
2
W = - P DV
E = hf
WAVES AND OPTICS
A = pr 2
C = 2 pr
Rectangular solid
V = wh
Cylinder
V = pr 2
S = 2 pr + 2 pr 2
Sphere
V =
A=
C=
V=
S =
b =
h =
=
w=
r =
area
circumference
volume
surface area
base
height
length
width
radius
Right triangle
c 2 = a 2 + b2
a
sin q =
c
b
cos q =
c
a
tan q =
b
4 3
pr
3
S = 4 pr 2
c
a
90°
q
b