Formula Sheet for Physics

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Reference Guide & Formula Sheet for Physics
         Dr. Hoselton & Mr. Price                                                                                   Page 1 of 8
                                                                               #20       Heating a Solid, Liquid or Gas
#3         Components of a Vector                                                                   Q = mcT (no phase changes!)
                if   V = 34 m/sec 48                                                                               Q = the heat added
                                    then                                                                              c = specific heat.
     Vi = 34 m/sec(cos 48); and VJ = 34 m/sec(sin 48)                                                   T = temperature change, K
                                                                               #21       Linear Momentum
#4        Weight = mg                                                                   momentum = p = mv = mass  velocity
         g = 9.81m/sec near the surface of the Earth                                            momentum is conserved in collisions
          = 9.795 m/sec in Fort Worth, TX
                                                                               #23       Center of Mass  point masses on a line
           Density = mass / volume                                                                xcm = (mx) / Mtotal

                     =
                            m
                            V
                                (
                              unit : kg / m 3       )                          #25       Angular Speed vs. Linear Speed
                                                                                             Linear speed = v = r = r  angular speed
#7       Ave speed = distance / time = v = d/t
       Ave velocity = displacement / time = v = d/t                            #26       Pressure under Water
       Ave acceleration = change in velocity / time                                                   P = gh
                                                                                                                     h = depth of water
#8         Friction Force                                                                                            = density of water
                         FF = FN                                             #28       Universal Gravitation
       If the object is not moving, you are dealing with static                                             m1 m2
          friction and it can have any value from zero up to s FN                                  F =G
       If the object is sliding, then you are dealing with kinetic
                                                                                                             r2
          friction and it will be constant and equal to K FN                                                    G = 6.67 E-11 N m / kg

#9         Torque                                                              #29       Mechanical Energy
                                                                                                PEGrav = P = mgh
                       = FLsin                                                                KELinear = K = mv
           Where  is the angle between F and L; unit: Nm
                                                                               #30       Impulse = Change in Momentum
#11        Newton's Second Law                                                                      Ft = (mv)
                    Fnet = FExt = ma
                                                                               #31       Snell's Law
#12        Work = FDcos                                                                         n1sin 1 = n2sin 2
                     Where D is the distance moved and                                   Index of Refraction
                         is the angle between F and the                                                 n=c/v
                                    direction of motion,                                                  c = speed of light = 3 E+8 m/s
                                                 unit : J
                                                                               #32       Ideal Gas Law
#16        Power = rate of work done                                                                 PV = nRT
                                           Work                                                                     n = # of moles of gas
                         Power =                             unit : watt                                            R = gas law constant
                                           time                                                                        = 8.31 J / K mole.
           Efficiency = Workout / Energyin                                     #34       Periodic Waves
      Mechanical Advantage = force out / force in                                                     v = f 
                   M.A. = Fout / Fin                                                                   f=1/T         T = period of wave

#19        Constant-Acceleration Linear Motion                                 #35       Constant-Acceleration Circular Motion
                      v = v + at            x                                                     =  + t               
                  (x-x) = vt + at       v                                                  -= t + t            
                                                                                                   2     2
                     v  = v + 2a (x - x) t                                                     =  + 2(-) t
                  (x-x) = ( v + v) t      a                                                  - = ( + )t            
                  (x-x) = vt - at       v                                                  - = t - t           

                                                                     Version 5/12/2005
                Reference Guide & Formula Sheet for Physics
        Dr. Hoselton & Mr. Price                                                                             Page 2 of 8
                                                                #53         Resistor Combinations
#36       Buoyant Force - Buoyancy                                                       SERIES
      FB = Vg = mDisplaced fluidg = weightDisplaced fluid                       Req = R1 + R2+ R3+. . .
                              = density of the fluid                                   PARALLEL
                                                                                                                n
                            V = volume of fluid displaced                       1     1   1       1                   1
                                                                               R eq
                                                                                    =   +
                                                                                      R1 R 2
                                                                                             +K +
                                                                                                  Rn
                                                                                                     =         R
                                                                                                               i =1   i
#37       Ohm's Law
                         V = IR                                #54         Newton's Second Law and
                   V = voltage applied                                           Rotational Inertia
                   I = current                                                           = torque = I
                   R = resistance                                         I = moment of inertia = mr (for a point mass)
                                                                          (See table in Lesson 58 for I of 3D shapes.)
          Resistance of a Wire
                       R = L / Ax                              #55         Circular Unbanked Tracks
                  = resistivity of wire material
                                                                                          mv 2
                 L = length of the wire                                                        = mg
                Ax = cross-sectional area of the wire                                      r
                                                                #56         Continuity of Fluid Flow
#39       Heat of a Phase Change                                                       Ainvin = Aoutvout                   A= Area
                    Q = mL                                                                                               v = velocity
                    L = Latent Heat of phase change             #58         Moment of Inertia       -       I
                                                                             cylindrical hoop              mr2
#41       Hooke's Law                                                        solid cylinder or disk     mr2
                                                                                                       2
                        F = kx                                              solid sphere                /5 mr2
          Potential Energy of a spring                                       hollow sphere              mr2
                                                                                                    1
           W = kx = Work done on spring                                  thin rod (center)        /12 mL2
                                                                             thin rod (end)             mL2
#42       Electric Power
                   P = IR = V  / R = IV                     #59         Capacitors      Q = CV
                                                                                 Q = charge on the capacitor
#44       Speed of a Wave on a String                                            C = capacitance of the capacitor
                                 mv 2                                            V = voltage applied to the capacitor
                        T=                                                  RC Circuits (Discharging)
                                  L                                                                 - t/RC
                                                                                         Vc = Voe
                                        T = tension in string
                                                                                          Vc - IR = 0
                                        m = mass of string
                                        L = length of string
                                                                #60         Thermal Expansion
#45       Projectile Motion
                                                                                 Linear: L = LoT
                   Horizontal: x-x= vt + 0
                   Vertical: y-y = vt + at                                  Volume: V = VoT

#46       Centripetal Force                                     #61         Bernoulli's Equation
                         mv  2                                                  P + gh + v  = constant
                   F=       = m 2 r                                        QVolume Flow Rate = A1v1 = A2v2 = constant
                          r
                                                                #62         Rotational Kinetic Energy (See LEM, pg 8)
#47       Kirchhoff's Laws                                                                            2
                                                                              KErotational = I = I (v / r)2
           Loop Rule: Around any loop Vi = 0                                                                       2
                                                                             KErolling w/o slipping = mv2 + I
           Node Rule: at any node Ii = 0

#51       Minimum Speed at the top of a                               Angular Momentum = L = I = mvrsin 
                Vertical Circular Loop                                  Angular Impulse equals
                                                                        CHANGE IN Angular Momentum
                         v = rg                                                 L = orquet = (I)

                                                      Version 5/12/2005
             Reference Guide & Formula Sheet for Physics
      Dr. Hoselton & Mr. Price                                                                                     Page 3 of 8
                                                                    #75        Thin Lens Equation
#63    Period of Simple Harmonic Motion                                                                                       f = focal length
            T = 2
                      m           where k = spring constant                         1   1    1  1 1  i = image distance
                                                                                      =    +   = +
                      k                                                             f   D o D i o i o = object distance
                                           f = 1 / T = 1 / period
#64    Banked Circular Tracks                                                              Magnification
                  v2 = rgtan                                                      M = - D i / Do = - i / o = H i / Ho

#66    First Law of Thermodynamics                                  Helpful reminders for mirrors and lenses
                 U = QNet + WNet                                    Focal Length of:      positive                 negative
       Change in Internal Energy of a system =                        mirror              concave                  convex
                          +Net Heat added to the system              lens               converging                                    diverging
                          +Net Work done on the system              Object distance = o all objects
                                                                    Object height = Ho    all objects
       Flow of Heat through a Solid                                 Image distance = i    real                     virtual
               Q / t = kAT / L                                    Image height = Hi     virtual, upright         real, inverted
                            k = thermal conductivity                Magnification         virtual, upright         real, inverted
                           A = area of solid
                           L = thickness of solid                   #76        Coulomb's Law
                                                                                                          q1 q 2
#68    Potential Energy stored in a Capacitor                                                    F =k
                   P = CV                                                                                r2
                                                                                                 1   N m2
                                                                                         k=             = 9E9
       RC Circuit formula (Charging)                                                     4 o           C2
                                  - t / RC
             Vc = Vcell(1 - e             )                        #77        Capacitor Combinations
                                  RC =  = time constant                                  PARALLEL
             Vcell - Vcapacitor - IR = 0                                            Ceq = C1 + C2+ C3 + ...
                                                                                           SERIES
                                                                                                                        n
                                                                                     1     1   1       1                      1
#71    Simple Pendulum                                                              C eq
                                                                                         =   +
                                                                                           C1 C 2
                                                                                                  +K +
                                                                                                       Cn
                                                                                                          =           Ci =1       i
                   L and f = 1/ T
           T = 2
                   g                                                #78        Work done on a gas or by a gas
                                                                                          W = PV
#72    Sinusoidal motion
          x = Acos(t) = Acos(2f t)                            #80        Electric Field around a point charge
                               = angular frequency                                                           q
                                                                                                     E=k
                                       f = frequency                                                         r2
#73    Doppler Effect                                                                            1   N m2
                                                                                         k =            = 9E9
                          343    Toward
                                           vo                                           4 o            C2
                 f= f
                                  Away

                          343 m   Toward
                                  Away     vs                       #82        Magnetic Field around a wire
       vo = velocity of observer: vs = velocity of source                                         I
                                                                                             B= o
                                                                                                 2 r
#74    2nd Law of Thermodynamics                                                         Magnetic Flux
       The change in internal energy of a system is                                       = BAcos 
       U = QAdded + WDone On  Qlost  WDone By
                                                                               Force caused by a magnetic field
       Maximum Efficiency of a Heat Engine                                             on a moving charge
       (Carnot Cycle) (Temperatures in Kelvin)                                           F = qvBsin 
                             Tc
             % Eff = (1 -       ) 100%                              #83     Entropy change at constant T
                             Th                                                           S = Q / T
                                                                    (Phase changes only: melting, boiling, freezing, etc)

                                                         Version 5/12/2005
              Reference Guide & Formula Sheet for Physics
      Dr. Hoselton & Mr. Price                                                                       Page 4 of 8
                                                               #95      Relativistic Time Dilation
#84     Capacitance of a Capacitor                                                    t = to / 
                  C = oA / d
                     = dielectric constant                     #96      Relativistic Length Contraction
                    A = area of plates                                                x = xo
                     d = distance between plates
                    o = 8.85 E(-12) F/m                                 Relativistic Mass Increase
                                                                                      m = mo / 
#85     Induced Voltage                 N = # of loops
                                                               #97       Energy of a Photon or a Particle
                    Emf = N                                                           E = hf = mc2
                               t
Lenz's Law  induced current flows to create a B-field                  h = Planck's constant = 6.63 E(-34) J sec
opposing the change in magnetic flux.                                          f = frequency of the photon

#86     Inductors during an increase in current                #98      Radioactive Decay Rate Law
                                                                                  -kt
                 VL = Vcelle
                             - t / (L / R)                                A = Aoe    = (1/2n)A0 (after n half-lives)
                                                                              Where k = (ln 2) / half-life
                                  - t / (L / R)
             I = (Vcell/R)[ 1 - e            ]                #99      Blackbody Radiation and
                                    L / R =  = time constant                    the Photoelectric Effect
#88     Transformers                                                    E= nhf where h = Planck's constant
                     N 1 / N 2 = V 1 / V2
                        I1V1 = I2V2                          #100     Early Quantum Physics
#89     Decibel Scale                                                   Rutherford-Bohr Hydrogen-like Atoms
        B (Decibel level of sound) = 10 log ( I / Io )
            I = intensity of sound                                            1    1    1 
            Io = intensity of softest audible sound
                                                                              = R     - 2  meters -1
                                                                                    2
                                                                                   ns n 
                                                                                           or
#92     Poiseuille's Law
                 P = 8LQ/(r )
                                      4
                                                                                  c      1    1 
                                                                            f =    = cR     - 2  Hz
                          = coefficient of viscosity                                      2
                                                                                         ns n 
                         L = length of pipe                                    R = Rydberg's Constant
                         r = radius of pipe                                       = 1.097373143 E7 m-1
                        Q = flow rate of fluid                                 ns = series integer (2 = Balmer)
        Stress and Strain                                                      n = an integer > ns
             Y or S or B = stress / strain
                      stress = F/A                                      Mass-Energy Equivalence
        Three kinds of strain: unit-less ratios                                       mv = mo / 
                   I. Linear: strain = L / L                             Total Energy = KE + moc2 = moc2 / 
                  II. Shear: strain = x / L                             Usually written simply as   E = m c2
                 III. Volume: strain = V / V
                                                                         de Broglie Matter Waves
#93     Postulates of Special Relativity                                For light:      Ep = hf = hc /  = pc
        1. Absolute, uniform motion cannot be
           detected.                                                        Therefore, momentum: p = h / 
        2. No energy or mass transfer can occur                          Similarly for particles, p = mv = h / ,
           at speeds faster than the speed of light.                    so the matter wave's wavelength must be
                                                                                       =h/mv
#94     Lorentz Transformation Factor                                    Energy Released by Nuclear
                           v2                                            Fission or Fusion Reaction
                    = 1- 2                                                             E = moc2
                           c

                                                    Version 5/12/2005
              Reference Guide & Formula Sheet for Physics
    Dr. Hoselton & Mr. Price                                                                    Page 5 of 8

MISCELLANEOUS FORMULAS                                 Fundamental SI Units
                                                       Unit        Base Unit                   Symbol
                Quadratic Formula                                         .........................
                if a x + b x + c = 0                  Length             meter                m
                         then
                                                       Mass               kilogram             kg
                    - b  b - 4ac
                                2
                                                       Time               second               s
               x=
                          2a                           Electric
                                                         Current          ampere               A
          Trigonometric Definitions                    Thermodynamic
     sin  = opposite / hypotenuse                        Temperature      kelvin               K
     cos  = adjacent / hypotenuse                      Luminous
     tan  = opposite / adjacent                          Intensity        candela              cd
                                                       Quantity of
             sec  = 1 / cos  = hyp / adj                 Substance        moles                mol
             csc  = 1 / sin  = hyp / opp
             cot  = 1 / tan  = adj / opp               Plane Angle        radian               rad

       Inverse Trigonometric Definitions               Solid Angle        steradian            sr or str
                = sin-1 (opp / hyp)
                = cos-1 (adj / hyp)
                = tan-1 (opp / adj)                    Some Derived SI Units
                                                       Symbol/Unit Quantity                    Base Units
                  Law of Sines                                            .........................
         a / sin A = b / sin B = c / sin C             C coulomb          Electric Charge As
                         or
         sin A / a = sin B / b = sin C / c             F farad            Capacitance          A2s4/(kgm2)

                 Law of Cosines                        H henry            Inductance           kgm2/(A2s2)
        a = b + c2 - 2 b c cos A
         2      2

        b2 = c2 + a2 - 2 c a cos B                     Hz hertz           Frequency            s-1
        c = a + b - 2 a b cos C
                                                       J   joule          Energy & Work kgm2/s2 = Nm
                     T-Pots
          For the functional form                      N newton           Force                kgm/s2
                     1 1 1
                      = +                               ohm               Elec Resistance kgm2/(A2s2)
                     A B C
                                                       Pa pascal          Pressure             kg/(ms2)
  You may use "The Product over the Sum" rule.
                          B C                          T tesla            Magnetic Field       kg/(As2)
                    A=
                          B+C
                                                       V volt             Elec Potential       kgm2/(As3)
        For the Alternate Functional form
                    1 1 1                              W watt             Power                kgm2/s3
                     = -
                    A B C                              Non-SI Units
                                                       o
                                                        C degrees Celsius            Temperature
             You may substitute T-Pot-d
                    B C    B C                         eV electron-volt              Energy, Work
              A=        =-
                    C-B    B-C

                                             Version 5/12/2005
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