Physics cheat sheet for high school students (M J Rhoades) This cheat sheet is broken down into three sections. 1) The equations with descriptions 2) ...
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Physics cheat sheet for high school students (M J Rhoades) This cheat sheet is broken down into three sections. 1) The equations with descriptions 2) Examples of how to solve the classic physics problems, and 3) definitions
Equations Motion (Constant acceleration) Vave
a=
=
where: Vave = average velocity in m/sec d = distance in meters t = time in seconds where:
a = acceleration in m/sec
2
t = time of the change in seconds = change in velocity m/sec
vf = vi + at where: vf = final velocity in m/sec vi = initial velocity in m/sec 2 a = acceleration in m/sec t = time under the acceleration in seconds
d = vit +
2
at
2
where: d = distance or displacement in meters vi = initial velocity in m/sec t = time in seconds 2 a = acceleration in m/sec
2
V f = V i + 2ad where: Vf = final velocity Vi = initial velocity a = acceleration d = distance or displacement
Derivation of motion formulas: Algebra
a=
= with t = 0 i
at = v – vi
vave =
v = vi + at
= = (
Now: v = (vi + at) from above, substituting for v i in the
equation.
= = v t + at 2
i
For the time independent formula From above: v = vi + at
t =
substituting
= v + a Factoring the fraction out = = = = v = v + 2ad i
2
2 i
Derivation of motion equations: Calculus Note; I used d for distance so don’t be confused when you see dd this is just the change in d
Ay = A sin θ where: Ay = any vector quantity acting along y axis (vertical) A = any vector quantity θ = angle of vector Ax = A cos θ where: Ax = any vector quantity acting along x axis (horizontal) A = any vector quantity θ = angle of vector
a=
where: a = acceleration in m/sec
2
Fnet = net force in newtons (newton =
)
m = mass in kg
Ff = µFn where: Ff = force of friction in newtons µ = coefficient of friction no units Fn = normal force in newtons
Fg
=
where: Fg = force due to gravity in newtons r = distance between object centers in meters G = universal gravitational constant 6.67 x 10
m1and2 = mass of objects in kg
g=
where: g = acceleration due to gravity in m/sec
2
Fg = weight or force due to gravity in newtons m = mass in kg
-11
ρ = mv
where : ρ = momentum in kg m/sec m = mass in kg v = velocity in m/sec
J = Fnett =
where: J = impulse in newton seconds
Fnet = net force in newtons t = time net force applied in seconds = change in momentum
Fs = k x where: Fs = force on a spring in newtons k = spring constant in
x = change in spring length from equilibrium in meters
PEs =
kx
2
where: PEs = potential energy of spring in newton meters or joules k = spring constant in newton / meters x = change in spring length in meters
Fc = mac where: Fc = centripetal force in newtons m = mass in kg 2 ac = centripetal acceleration meters/sec
ac
=
where: ac = centripetal acceleration in meters/sec
2
v = velocity in meters/sec r = radius in meters
PE = mg h where: PE = change in potential energy in newton meters m = mass in kg 2 g = acceleration due to gravity in meter/sec h = change in height in meters
KE = mv
2
where: KE = kinetic energy in newton meters or joules m = mass in kg v = velocity in meters/sec
W = Fd = ET where: W = work in newton meters F = force in newtons d = distance in meters ET = total energy in newton meters
ET = PE + KE + Q where: ET = total energy in newton meters PE = potential energy in newton meters KE = kinetic energy in newton meters Q = internal energy in newton meters
P= = = Fv
avg
where: P = power in watts or newton meters/second
W = work in newton meters F = force in newtons d = distance in meters t = time in seconds Vavg = average velocity in meters/sec Remember a newton meter = joule
v = λ where: v = velocity in meters/sec
= frequency in hertz or cycles/sec λ = wave length in meters
T=
where: T = the period which is the reciprocal of the frequency or seconds/cycle
= frequency in cycles/second or hertz
θi = θr where: θi = angle of incidence
n=
θr = angle of refraction where: n = the absolute index of refraction no units 8
c = speed of light 3 x 10 meters/sec v = velocity or speed in a medium
n1 sin θ1 = n2 sin θ2 where: n1+2 = index of refractions for the light (no units) θ1+2 = angles of the light in degrees
= =
where: n = index of refraction (no units)
Ephoton = h =
v = to velocity in meters/sec λ = wave length in meters where: Ephoton = energy of the photon in electron volts or joules -19
1 electron volt = 1.602 x 10 joules Ephoton = Ei - Ef = initial energy - final energy (in electron volts) -34 h = planks constant (6.63 x 10 joule seconds) = frequency in cycles/sec or hertz 8 c = speed of light (3 x 10 meters/sec)
λ = wave length in meters E = m c where: E = energy in joules or newton meters m = mass in kg 8 c = speed of light 3 x 10 meters/sec -27 1 amu = 1.66 x 10 kg 2
Fe =
where: Fe = electrostatic force in newtons k = Boltzman's constant (8.99 x 10
9
)
this C is not the speed of light its coulombs q1+2 = charge of the two objects in coulombs 18 1 coulomb is equal the charge of = 6.25 x 10 protons or electrons r = distance between the centers of the two objects in meters
Pe (Mev) =
where: Pe = potential energy of one particle to the other in Mev
q1&2 = charge of the two particles in coulombs r = distance between centers of the particles in meters -19 1 ev = 1.602 x 10 joules -13 1 Mev = 1.602 x 10 joules
E=
V=
where: E = electric field strength newtons/coulomb
where: V = potential difference in volts
Fe = electrostatic force in newtons q = charge in coulombs
W = (electrical energy) work in joules q = charge in coulombs ie when one joule of work moves one coulomb of charge, there is a potential difference of on volt.
I=
where: I = electric current in amperes q = change in charge in coulombs (6.25 x 10 t = time in seconds
V = I R Where: V = volts in volts I = current in amperes R = resistance in ohms
18
electrons)
R=
where: R = resistance in ohms p = resistivity in ohm meters L = length of conductor in meters 2 A = cross sectional area in meter
P = VI = I R = 2
where: P = power in watts
W = Pt = VIt = I Rt = 2
V = voltage in volts I = current in amperes R = resistance in ohms t = time in seconds
where: W = work in joules P = power in watts t = time in seconds V = volts in volts I = current in amperes R = resistance in ohms