Download 2006, 2007 Table of Information and Equation Tables for AP Physics

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 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.
TABLE OF INFORMATION FOR 2006 and 2007
CONSTANTS AND CONVERSION FACTORS
UNITS
1u
1 unified atomic mass unit,
931 MeV c
2
mp
1.67 – 10 27 kg
Neutron mass,
mn
1.67 – 10 27 kg
Electron mass,
me
9.11 – 10 31 kg
Electron charge magitude,
Avogadro’s number,
Universal gas constant,
e
1.60 – 10 19 C
Proton mass,
N0
R
Boltzmann’s constant,
kB
Speed of light,
c
Planck’s constant,
h
Name
1.66 – 10 27 kg
8.31 J (mol <K)
1.38 – 10
23
J K
6.63 – 10
kilogram
kg
second
s
ampere
A
hertz
3.00 – 10 m s
34
m
mole
8
J <s
Symbol
meter
kelvin
6.02 – 1023 mol -1
PREFIXES
K
mol
Hz
newton
N
pascal
Pa
15
hc
4.14 – 10
eV <s
25
1.99 – 10
J <m
Vacuum permittivity,
⑀0
1.24 – 103 eV<nm
8.85 – 10 12 C2 N <m 2
Coulomb’s law constant,
1 4 p⑀0
k
Vacuum permeability,
Magnetic constant, k „
m0
m0 4 p
Universal gravitational constant,
Acceleration due to gravity
at Earth’s surface,
G
1 atmosphere pressure,
1 atm
1 electron volt,
g
1 eV
joule
J
watt
W
coulomb
C
volt
V
4 p – 10 7 (T <m) A
ohm
W
10 7 (T <m) A
henry
H
farad
F
tesla
T
9
2
9.0 – 10 N <m C
6.67 – 10
9.8 m s
11
m
3
2
2
kg<s2
1.0 – 105 N m 2
degree
Celsius
1.0 – 105 Pa
1.60 – 10 19 J
electronvolt
DC
Prefix
Symbol
10
9
giga
G
10
6
mega
M
10
3
kilo
k
10
2
centi
c
10
3
milli
m
10
6
micro
m
10
9
nano
n
10
12
pico
p
Factor
VALUES OF
TRIGONOMETRIC
FUNCTIONS FOR COMMON
ANGLES
T
0
sin T cos T
D
tan T
0
1
0
30D
1/2
3 /2
3 /3
37D
3/5
4/5
3/4
45D
2 /2
2 /2
1
53D
4/5
3/5
4/3
60D
3 /2
1/2
3
90D
1
0
f
eV
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.
ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2006 and 2007
NEWTONIAN MECHANICS
u
u0 at
x
x0 u0 t u2
u0 2 2a x x0 ÇF
Fnet
ma
F fric … m N
ac
u2
r
t
r F sin q
p
mv
J
K
FDt
Dp
1 2
mu
2
DUg
W
mgh
F Dr cos q
W
Dt
Pavg
P
F u cos q
Fs
k x
Us
1 2
at
2
1 2
kx
2
Ts
2p
m
k
Tp
2p
A
g
T
1
f
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
C
C
Uc
UG
Gm1m2
r2
Gm1m2
r
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
i
1
i
i
i
1
Rp
ÇR
FB
qu B sin q
FB
BI A sin q
B
FG
Eavg
V
1 q1q2
4 p⑀0 r
qV
fm
eavg
e
1
i
i
m0 I
2p r
BA cos q
BAu
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 2006 and 2007
FLUID MECHANICS AND THERMAL PHYSICS
P0 r gh
P
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
PDV
W
DU
const.
Q W
e
W
QH
ec
TH TC
TH
3k B T
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 = density
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
hf f
K max
l
DE
pc
h
p
( Dm ) c 2
E=
f =
K=
m=
p =
l=
f=
energy
frequency
kinetic energy
mass
momentum
wavelength
work function
WAVES AND OPTICS
u
fl
n
c
u
n 1 sin q1
n 2 sin q2
n2
n1
sin qc
1
1
si s0
hi
M
h0
R
2
d sin q
1
f
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 Aw h
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
ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2006 and 2007
MECHANICS
u
u0 at
x
x0 u0 t u2
ÇF
1 2
at
2
u02 2a x x0 Fnet
F
dp
dt
J
Ô F dt
p
mv
ma
Dp
F fric … m N
W
ÔF
K
1 2
mu
2
P
dW
dt
P
Fⴢv
DUg
ac
t
Çt
I
rcm
™
dr
mgh
u2
r
ELECTRICITY AND MAGNETISM
t net
2
Ô r dm
L
r–p
K
1 2
Iw
2
E
F
q
Fs
k x
Uc
1
QV
2
Ia
Us
1 2
kx
2
R
rA
A
Ç mr
E
rJ
I
Neud A
V
IR
2
T
2p
w
1
f
Ç mr Ç m
rw
1 q1q2
4 p⑀ 0 r 2
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
Ts
Iw
w
w0 at
q
q0 w0t Tp
FG
1 2
at
2
UG
m
k
2p
2p
Gm1m2
r2
Gm1m2
r
rˆ
dV
dr
V
1
4 p⑀0
UE
q
Ç rii
1 q1q2
4 p⑀0 r
Q
V
C
k⑀0 A
d
Cp
Ç Ci
1
Cs
ÇC
I
1
Rp
P
FM
i
1
i
F
I
J
L
A
n
=
=
=
=
=
=
=
=
=
=
=
=
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
i
qV
C
Rs
A
g
⑀0
E
A
B
C
d
E
e
Q
vÔ E ™ d A
w2 r
r–F
u
F
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 =
i
dQ
dt
Ç Ri
1
CV 2
2
N =
P
Q
q
R
r
t
U
=
=
=
=
=
=
=
V=
u =
r =
fm =
k =
vÔ B
™
d
m0 I d – r
4p r 3
dB
F
Ô I d – B
Bs
m0 nI
fm
ÔB
i
1
ÇR
i
i
IV
qv – B
m0 I
dA
d fm
dt
e
e
L
UL
™
dI
dt
1 2
LI
2
ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2006 and 2007
GEOMETRY AND TRIGONOMETRY
Rectangle
A bh
Triangle
1
bh
2
A
Circle
pr2
A
2p r
Parallelepiped
V Aw h
Cylinder
C
V
p r 2A
S
2p r A 2p r 2
A=
C=
V=
S =
b =
h =
A=
w=
r =
CALCULUS
area
circumference
volume
surface area
base
height
length
width
radius
df
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
n
dx
1
x n 1 , n › 1
n 1
x
dx
ex
Ôx
Ôe
Sphere
d f du
du dx
V
4 3
pr
3
Ô
S
4p r 2
Ô cos x dx
sin x
Ô sin x dx
cos x
Right Triangle
a 2 b2
c2
sin q
a
c
cos q
b
c
tan q
a
b
c
q
a
90q
b
dx
x
ln x