Physics-Equations

Document Sample
Physics-Equations Powered By Docstoc
					                                                                    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
                                                               −7                                    farad                F
                                                                                                     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 ˆ 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
                                                                         Parallelepiped            r =   radius
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 ˆ mN                         m=    mass                      V=                                             n   =   number of loops of wire per
                                                                       4p 0
W =        IF   œ   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
     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
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 ž -1

Ie x dx = e x

I   dx
     x
        = 1n x

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

				
DOCUMENT INFO
Shared By:
Stats:
views:253
posted:3/25/2010
language:English
pages:5