1.
TABLE OF INFORMATION FOR 2002
CONSTANTS AND CONVERSION FACTORS UNITS PREFIXES
= 1.66 10 -27 kg
Name Symbol Factor Prefix Symbol
1u
1 unified atomic mass unit,
10 9
meter m giga G
= 931 MeV/c 2
kilogram kg 10 6 mega M
m p = 1.67 × 10 −27 kg
Proton mass,
10 3
mn = 1.67 × 10 −27 kg second s kilo k
Neutron mass,
−2
−31
me = 9.11 × 10
Electron mass, kg centi c
ampere A 10
e = 1.60 × 10 −19 C −3
Magnitude of the electron charge, milli m
10
kelvin K
N0 = 6.02 × 10 23 mol −1
Avogadro’s number,
10 −6 µ
micro
mole mol
R = 8.31 J / ( mol ¼ K )
Universal gas constant,
10 −9 nano n
hertz Hz
k B = 1.38 × 10 −23 J / K
Boltzmann’s constant,
−12
newton N pico p
10
c = 3.00 × 10 8 m / s
Speed of light,
h = 6.63 × 10 −34 J ⋅ s pascal Pa
Planck’s constant,
VALUES OF TRIGONOMETRIC FUNCTIONS
eV ⋅ s
−15
= 4.14 × 10 FOR COMMON ANGLES
joule J
θ sin θ cos θ tan θ
hc = 1.99 × 10 −25 J ⋅ m watt W
= 1.24 × 10 3 eV ⋅ nm o
coulomb C 0 1 0
0
C / N⋅m
−12
= 8.85 × 10 2 2
volt V
Vacuum permittivity, 0
30o 1/2 3 /2 3 /3
= 9.0 × 10 N ⋅ m / C Ω
ohm
k = 1 / 4π 9 2 2
Coulomb’s law constant, 0
µ 0 = 4π × 10 −7 (T ⋅ m ) / A henry H
37o
Vacuum permeability, 3/5 4/5 3/4
k
= µ 0 / 4π = 10 (T ⋅ m ) / A
−7 farad F
Magnetic constant,
45o 1
2 /2 2 /2
tesla T
= 6.67 10 -11 m 3 / kg ¼ s 2
Universal gravitational constant, G
degree
Acceleration due to gravity
53o
o
4/5 3/5 4/3
Celsius C
g = 9.8 m / s 2
at the Earth’s surface,
electron-
1 atm = 1.0 × 10 5 N / m 2
1 atmosphere pressure,
60o 1/2
3 /2 3
volt eV
= 1.0 × 10 5 Pa
∞
1 eV = 1.60 × 10 −19 J 90o
1 electron volt, 1 0
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.
2.
ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2002
NEWTONIAN MECHANICS ELECTRICITY AND MAGNETISM
u = u 0 + at q1 q 2
1
a= acceleration A =area
F=
4p
F= force B =magnetic field
r2
0
12
x = x0 + u0 t + f= frequency C =capacitance
at
2 F
E=
h= height d =distance
0 5 q
J= impulse E =electric field
u 2 = u 0 2 + 2a x - x 0 e emf
K= kinetic energy =
q1 q 2
1
UE = qV = F =force
k= spring constant 4p r
Ê F = Fnet = ma 0
l= length I =current
l
V
m= mass =length
E avg = −
F fric mN N= normal force P =power
d
P= power Q charge
=
∑r
qi
1
u2 V=
p= momentum q =point charge
ac = 4p
r 0 i
i
r= radius or distance R =resistance
r= position vector r =distance
Q
t = rF sin q C=
T= period t =time
V
p = mv t= time U potential (stored) energy
=
0A
C=
U= potential energy V =electric potential or
d
u=
J = FDt = Dp velocity or speed potential difference
1 1 u = velocity or speed
Uc = QV = CV 2
W= work done on a system
r = resistivity
2 2
x= position
1
mu 2
K= m= fm = magnetic flux
DQ
coefficient of friction
2
I avg =
q= angle Dt
DUg = mgh t= torque
ρl
R=
Dr = FDr cos q
W=F A
V = IR
P = IV
W
Pavg =
Dt
C p = ∑ Ci
P = F v = Fu cos q i
1 1
=∑
Fs = - k x Cs i Ci
Rs = ∑ Ri
12
Us = kx i
2
1 1
=∑
m
Ts = 2 p Rp i Ri
k
FB = qu B sin θ
l
Tp = 2 p
g
FB = BIl sin θ
1 m0 I
T= B=
f
2p r
Gm1m2
FG = - fm = B • A = BA cos θ
r2
Dfm
eavg = −
Gm1m2
UG = - Dt
r
e = Blu
3.
ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2002
FLUID MECHANICS AND
WAVES AND OPTICS
THERMAL PHYSICS
p = p0 + rgh u = fl
A = area d = separation
Fbuoy = rVg c = specific heat or molar f = frequency or focal
c
n=
u
specific heat length
A1u1 = A2 u 2
e = efficiency h = height
n 1 sin q1 = n 2 sin q 2
1
p + rgy + ru 2 = const. F = force L = distance
n2
2
sin q c =
h = depth M= magnification
D l = a l 0 DT n1 m = an integer
Kavg = average molecular
1 1 1 n = index of refraction
kinetic energy
Q = mL + =
si s0 f
L = heat of transformation R = radius of curvature
Q = mcDT l = length s = distance
hi s
u = speed
=- i
M=
M= molecular mass
F s0
h0
p= m = mass of sample x = position
A
l = wavelength
R
n = number of moles
f=
pV = nRT q = angle
2
p = pressure
d sin q = ml
Q = heat transferred to a system
3
K avg = kT T = temperature ml L
2B xm
U = internal energy d
V = volume
3k B T
3 RT
u rms = =
m u = velocity or speed
M
urms = root-mean-square
W = - pDV velocity
Q = ncDT W = work done on a system
y = height GEOMETRY AND TRIGONOMETRY
DU = Q + W a = coefficient of linear
Rectangle A= area
expansion
DU = ncV DT A = bh C= circumference
µ = mass of molecule
Triangle
r = density V= volume
W
e= 1 S= surface area
A = bh
QH
2 b= base
TH - TC Circle h= height
ec = A = pr 2 l= length
TH
C = 2 pr w= width
Parallelepiped r= radius
V = lwh
ATOMIC AND NUCLEAR PHYSICS
E = hf = pc Cylinder
E = energy
V = pr 2 l
f = frequency
Kmax = hf − f S = 2 pr l + 2 pr 2
K = kinetic energy
Sphere
= mass
m
h
l= 4
V = pr 3
p = momentum
p 3
l = wavelength
S = 4 pr 2
DE = ( Dm) c 2 f = work function
Right Triangle
a 2 + b2 = c2 c a
a
sin q = q 90
c
b
b
cos q = c
a
tan q = b
4.
ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002
MECHANICS ELECTRICITY AND MAGNETISM
u = u 0 + at q1 q 2
1
a= acceleration A = area
F=
4p
F= force B = magnetic field
r2
12
x = x0 + u 0 t + 0
at
f= frequency C = capacitance
2
0 5
F
E=
u 2 = u 0 2 + 2a x - x 0 h= height d = distance
q
I= rotational inertia E = electric field
Ê F = Fnet = ma
e
Q
J= impulse emf
E • dA = =
dp
F= F = force
K= kinetic energy 0
dt
I I = current
k= spring constant dV
J = F dt = Dp E=−
l= length L = inductance
dr
p = mv l
L= angular momentum = length
∑r
qi
1
F fric mN V=
m= mass n = number of loops of wire per
4p 0
IF N= normal force unit length
i
i
W= dr
P= power P= power
q1 q 2
1
UE = qV =
1
mu 2
K= p= momentum Q= charge
4p r
0
2 r= radius or distance q= point charge
Q
dW C=
P= r= position vector R= resistance
dt V
T= period r= distance
P= kA
Fv
t= time t= time
C= 0
DU g = mgh d
U= potential energy U= potential or stored energy
C p = ∑ Ci
u=
u 2 = w2r velocity or speed V= electric potential
ac = u=
i
W= work done on a system velocity or speed
r
t=rF r=
1 1 resistivity
x= position
=∑
m=
Ê t = t net = Ia fm =
coefficient of friction magnetic flux
Cs i Ci
I k=
q= angle dielectric constant
I = r 2 dm = Ê mr 2 dQ
I=
t= torque
rcm = Ê mr Ê m dt
w= angular speed
u = rw 1 1
a= Uc = QV = CV 2
angular acceleration
L = r p = Iw 2 2
rl
1 R=
K = Iw 2
A
2
w = w0 + at V = IR
Rs = ∑ Ri
q = q 0 + w0 t + 1 at 2
2 i
Fs = - kx 1 1
=∑
1 Rp i Ri
Us = kx 2
2
P = IV
2p 1
T= =
w FM = qv × B
f
B • d ø = m0 I
m
Ts = 2 p
I
k
F = I dø × B
l
Tp = 2 p
Bs = m0 nI
g
I
Gm1m2
fm = B • dA
$
FG = - r
r2
dfm
e=−
Gm1m2
UG = - dt
r
dI
e = −L
dt
12
U L = LI
2
5.
ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002
GEOMETRY AND TRIGONOMETRY
Rectangle A= area
A = bh C= circumference
Triangle V= volume
1 S= surface area
A = bh
2 b= base
Circle
h= height
A = pr 2 l= length
C = 2 pr w= width
Parallelepiped r= radius
V = lwh
Cylinder
V = pr 2 l
S = 2 prl + 2 pr 2
Sphere
4
V = pr 3
3
S = 4 pr 2
Right Triangle
a 2 + b2 = c2 c a
a
sin q = q 90
c
b
b
cos q =
c
a
tan q =
b
CALCULUS
df d f du
=
dx du dx
27 n -1
dn
x = nx
dx
27
dx
e = ex
dx
d 1
(1n x) =
dx x
d
(sin x) = cos x
dx
d
(cos x) = - sin x
dx
I 1 n +1
xn dx = , n -1
x
n +1
Ie x dx = e x
I dx
= 1n x
x
I cos x dx = sin x
I sin x dx = - cos x
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