## 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
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

Inverse Trigonometric Definitions               Solid Angle        steradian            sr or str
= sin-1 (opp / 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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