# Physics-Equations by manish6118

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```									                                                                    TABLE OF INFORMATION FOR 2002

CONSTANTS AND CONVERSION FACTORS                                                                   UNITS                          PREFIXES

= 1.66  10 -27 kg
Name         Symbol        Factor     Prefix   Symbol
1 unified atomic mass unit,            1u
meter                m     10 9       giga      G
= 931 MeV/c 2
kilogram          kg       10 6       mega      M
Proton mass,               m p = 1.67 × 10 −27 kg
Neutron mass,               mn = 1.67 × 10 −27 kg                                second               s     10 3       kilo      k
Electron mass,              me = 9.11 × 10             −31
kg                                                   −2
ampere               A     10         centi     c
Magnitude of the electron charge,                  e = 1.60 × 10 −19 C                                                         10   −3
milli     m
kelvin               K
Avogadro’s number,                N0 = 6.02 × 10 23 mol −1
mole             mol       10 −6      micro        µ
Universal gas constant,                 R = 8.31 J / ( mol ¼ K )
hertz            Hz        10 −9      nano      n
Boltzmann’s constant,                  k B = 1.38 × 10 −23 J / K
newton               N          −12
Speed of light,                  c = 3.00 × 10 8 m / s                                                       10         pico      p
Planck’s constant,                 h = 6.63 × 10 −34 J ⋅ s                           pascal            Pa
VALUES OF TRIGONOMETRIC FUNCTIONS
= 4.14 × 10      −15
eV ⋅ s                                               FOR COMMON ANGLES
joule                J
hc = 1.99 × 10 −25 J ⋅ m                              watt              W          θ        sin θ     cos θ         tan θ
= 1.24 × 10 3 eV ⋅ nm                       coulomb              C      0
o
0               1       0
Vacuum permittivity,                    0   = 8.85 × 10      −12
C / N⋅m
2           2
volt                 V
30o        1/2              3 /2    3 /3
Coulomb’s law constant,      k = 1 / 4π    0    = 9.0 × 10 N ⋅ m / C
9                  2   2       ohm               Ω

Vacuum permeability,                   µ 0 = 4π × 10 −7 (T ⋅ m ) / A                     henry                H
37o        3/5       4/5           3/4
Magnetic constant,      k
= µ 0 / 4π = 10 (T ⋅ m ) / A
tesla                T     45o          2 /2           2 /2    1
Universal gravitational constant,                G     = 6.67  10 -11 m 3 / kg ¼ s 2
degree
Acceleration due to gravity
at the Earth’s surface,                  g = 9.8 m / s     2                                Celsius        o
C     53o        4/5       3/5           4/3
1 atmosphere pressure,            1 atm = 1.0 × 10 5 N / m 2
electron-
volt           eV        60o          3 /2    1/2            3
= 1.0 × 10 5 Pa
1 electron volt,           1 eV = 1.60 × 10 −19 J                                                            90o             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.
ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2002

NEWTONIAN MECHANICS                                                           ELECTRICITY AND MAGNETISM
u = u 0 + at                                  a =   acceleration                    1            q1 q 2                    A   =area
F=
F =   force                          4p        0    r2                       B   =magnetic field
1 2
x = x0 + u0 t +                    at         f =   frequency                                                              C   =capacitance
2                                                 F
h =   height                    E=                                           d   =distance
u 2 = u 0 2 + 2a x - x 0     0          5     J =
K =
impulse
kinetic energy
q
1             q1 q 2
E   =
e emf
=
electric field

k =   spring constant           UE = qV =                                    F   =force
4p               r
Ê F = Fnet = ma                               l =   length
0
I   =current
m=    mass
E avg = −
V                             l   =length
F fric  mN                                   N =   normal force                             d                             P   =power
P =   power                                                                      =
Q charge
∑r
1                  qi
u2                                     p =   momentum                  V=                                           q   =point charge
ac =                                                                               4p
r                                  r =   radius or distance                       0    i       i
R   =resistance
t = rF sin q                                  r =   position vector                Q                                       r   =distance
C=
T =   period                         V                                       t   =time
p = mv                                        t =   time
0A
=
U potential (stored) energy
U=    potential energy          C=                                           V   =electric potential or
d
J = FDt =               Dp                    u =   velocity or speed                                                                  potential difference
1    1                                   u = velocity or speed
W=    work done on a system     Uc = QV = CV 2
1                                      x =   position                      2    2                                    r = resistivity
K =      mu 2                                  m=                                                                          fm = magnetic flux
2                                            coefficient of friction             DQ
q =   angle                     I avg =
Dt
DUg = mgh                                     t =   torque
ρl
R=
W = F          Dr = FDr cos q                                                      A
V = IR
Pavg =
W                                                              P = IV
Dt
C p = ∑ Ci
P = F v = Fu cos q                                                                      i
1     1
=∑
Fs = - k x                                                                    Cs  i Ci

1 2                                                                Rs = ∑ Ri
Us =         kx                                                                         i
2
1     1
m                                                            =∑
Ts = 2 p                                                                      Rp  i Ri
k
l                                                         FB = qu B sin θ
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
UG = -
Gm1m2                                                         eavg = −
r                                                                              Dt
e = Blu
ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2002
FLUID MECHANICS AND
THERMAL PHYSICS                                 WAVES AND OPTICS

p = p0 + rgh                     A = area                           u = fl                        d = separation
Fbuoy = rVg                      c = specific heat or molar               c                       f = frequency or focal
n =
A1u1 = A2 u 2
specific heat                     u                              length
e = efficiency                     n 1 sin q1 = n 2 sin q 2      h = height
1
p + rgy + ru 2 = const.          F = force
n2
L = distance
2                   h = depth                          sin q c =                     M= magnification
D l = a l 0 DT                   Kavg = average molecular                       n1                m = an integer
Q = mL                                    kinetic energy            1    1    1                   n = index of refraction
+    =
L = heat of transformation         si   s0   f                   R = radius of curvature
Q = mcDT                         l = length                                                       s = distance
hi     s
M= molecular mass                  M =       = - i               u = speed
F                                                                   h0     s0
p =                              m = mass of sample                                               x = position
A
n = number of moles                      R                       l = wavelength
f =
pV = nRT                         p = pressure                             2                       q = angle
Q = heat transferred to a system   d sin q = ml
3
K avg =       k T                T = temperature                            ml L
2 B                                                     xm
U = internal energy                         d
3 RT     3k B T   V = volume
u rms =             =
M         m      u = velocity or speed
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
expansion                       Rectangle                 A=    area
DU = ncV DT                      µ = mass of molecule                        A = bh                C=    circumference
r = density                             Triangle                  V=    volume
W
e =                                                                               1                S =   surface area
QH                                                                    A = bh
2                b =   base
TH - TC                                                           Circle                    h =   height
ec =                                                                         A = pr 2              l =   length
TH
C = 2 pr               w=    width
ATOMIC AND NUCLEAR PHYSICS                                                  V = lwh
E = hf = pc                   E   =   energy                          Cylinder
f   =   frequency                          V = pr 2 l
Kmax = hf − f                                                            S = 2 pr l + 2 pr 2
K   =   kinetic energy
h                     m   =   mass                            Sphere
l =                           p   =   momentum                                 4
V = pr 3
p                                                                      3
l   =   wavelength
DE = ( Dm) c 2                 f   =   work function                      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
ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002

MECHANICS                                                        ELECTRICITY AND MAGNETISM
u = u 0 + at                        a =   acceleration                    1              q1 q 2                    A   =   area
F=
1 2                F =   force                          4p               r2                       B   =   magnetic field
x = x0 + u 0 t +   at                                                                0
2                  f =   frequency                                                                C   =   capacitance
0     5
F
u 2 = u 0 2 + 2a x - x 0            h =   height                    E=                                             d   =   distance
q
Ê F = Fnet = ma
I =   rotational inertia                                                       E   =   electric field
J =   impulse                    E • dA =
Q                         e   =   emf
dp
F =                                 K =   kinetic energy                                  0                        F   =   force
dt
I
J = F dt = Dp
k =
l =
spring constant
length                    E=−
dV
dr
I
L
=
=
current
inductance
p = mv                              L =   angular momentum                                                         l   =   length
∑r
1                     qi
F fric  mN                         m=    mass                      V=                                             n   =   number of loops of wire per
4p 0
W =        IF      dr
N =
P =
normal force
power
i

1
i

q1 q 2   P =     power
unit length
1                                                            UE = qV =
K =       mu 2                      p =   momentum                                        4p          0     r      Q=      charge
2                            r =   radius or distance                                                       q =     point charge
dW                                                               Q
P =                                 r =   position vector           C=                                             R =     resistance
dt                          T =   period                         V                                         r =     distance
P =    F v                                                              k A
t =   time                      C= 0                                           t =     time
DU g    = mgh                       U=    potential energy                 d                                       U=      potential or stored energy
u 2 = w2r                u =   velocity or speed         C p = ∑ Ci                                     V =     electric potential
ac =                                W=    work done on a system                  i                                 u =     velocity or speed
r
t=rF                               x =   position                  1
=∑
1                                         r =    resistivity
Ê t = t net = Ia                     m=   coefficient of friction   Cs  i Ci                                       fm =    magnetic flux
I
I = r 2 dm = Ê mr 2
q =
t =
angle
torque                    I=
dQ                                         k =     dielectric constant
rcm = Ê mr Ê m                      w=    angular speed                 dt
u = rw                              a =   angular acceleration            1  1
Uc = QV = CV 2
L = r  p = Iw                                                            2  2
1                                                                   rl
K = Iw 2                                                            R=
2                                                                   A
w = w0 + at                                                         V = IR
q = q 0 + w0 t + 1 at 2                                             Rs = ∑ Ri
2                                                               i
Fs = - kx                                                           1     1
=∑
1                                                            Rp  i Ri
Us = kx 2
2
2p       1                                                      P = IV
T =      =
w       f                                                      FM = qv × B

Ts = 2 p
m                                                          B • d ø = m0 I

Tp = 2 p
k
l                                                             I
F = I dø × B
g                                                        Bs = m0 nI

FG = -
Gm1m2
r2
\$
r                                                           I
fm = B • dA
dfm
UG = -
Gm1m2                                                      e=−
r                                                            dt
dI
e = −L
dt
1 2
U L = LI
2
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
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
d n
dx
2 7
x = nx
n -1

d x
dx   2 7
e = ex

d             1
(1n x) =
dx            x
d
(sin x) = cos x
dx
d
(cos x) = - sin x
dx
Ixn dx =
1 n +1
n +1
x    , n  -1

Ie x dx = e x

I   dx
x
= 1n x

I   cos x dx = sin x
I sin x dx = - cos x

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