x =?vt

?v = (v + vo)/2

v = vo + at

x = vot + ½at2

v2 = vo2 + 2ax

y =?vt

?v ’ ½(vo + v)

v = vo – gt

y = vot – ½gt2

v2= vo2 – 2gy

R = (v02/g)sin(2θ)

Forces

Fnet = maFgravity = mg

Ffriction ≤ μsNFfriction = μkN

Circular Motion

Fnet = mv2/rac = v2/r

v = 2πr/T

f = 1/TT = 1/f

Gravitation

F = GM1M2/R2g = GM/R2

T2/R3 = 4π2/GM = constant

GM = Rv2

Energy

W = FdcosθKE = ½mv2

PE = mghPE = ½kx2

PE0 + KE0 + W = PE + KE

P = W/t = E/t = Fv

Momentum

p = mv

ptot = p1 + p2 + …

ptot before = ptot after

FΔt = Δp = mv – mv0

xcm = (m1x1 + m2x2 + …)/(m1 + m2 + …)

vcm = (m1v1 + m2v2 + …)/(m1 + m2 + …)

Rotational Motion

θ ’ ?ωtω = (ωo + ω)/2

ω ’ ωο + αtθ ’ ωοt + ½αt2

ω2 ’ ωο2 + 2αθ

s = rθv = r ωatan = rα

τ = r x F

Ι ’ Σmr2Ιparallel = ICM + md2

Στ ’ ΙαL ’ Ιω

Στ ’ dL/dt L = r x p

ΚΕ ’ ½Ιω2

Bodies in Equilibrium

Στ ’ 0ΣF ’ 0

Harmonic Motion

F = -kx PE = ½kx2

½kx2 + ½mv2 = ½kA2 = ½mvmax2

x(t) = Asin(ωt)v(t) = Aω cos(ωt)

a(t) = -Aω2 sin(ωt)

ω = (k/m)1/2

x(t) = A cos(ωt)v(t) = -Aω sin(ωt)

a(t) = -Aω2 cos(ωt)

T = 2π(m/k) 1/2

T = 2π(L/g)1/2

f= 1/T T = 1/f

Waves

v = fλ

Ι ’ P/(4πr2)

│d1 – d2│ = 0, λ, 2λ, 3λ ....

│d1 – d2│ = λ/2, 3λ/2, 5λ/2 ....

v = (T/(m/L))½

f1 = v/2Lλ1 = 2L

fn = nf1λn = λ1/nn = 1, 2, 3, …..

Sound

β ’ 10log(1012Ι)

vsound = 331 + .6T(0C)

f = f0(v±v0)/(v±vs)

f1 = v/2Lλ1 = 2L

fn = nf1λn = λ1/nn = 1, 2, 3, …..

f1 = v/4L λ1 = 4L

fn = nf1 λn = λ1/nn = 1, 3, 5, ….

fB = │f1 – f2│

sinθ = vsound / vobject

Electrostatics

F = QEF = kQ1Q2/r2

E = kQ/r2

ΔPE = QΔVPE = kQ1Q2/r

V = kQ/rΔV = EΔx

C= Q/VC = ε0A/d

C = κC0E = Q/(ε0A)

U = ½QV = ½CV2 =½Q2/C

u= ½ε0E2

Circuits

I = ΔQ/ΔtV = IR

R = ρL/Aρ = ρ0[1+α(T-20oC)]

P = W/t = E/t (energy/time)

P = IV = I2R = V2/R

RS = R1 + R2 + …

1/RP = 1/R1 + 1/R2 + …

Vterminal = ε - IR

Cp = C1 + C2 + …

1/Cs = 1/C1 + 1/C2 + …

Vcharge = V0(1-e-t/RC)

Vdischarge = V0e-t/RC

τ = RC

Magnetism

F = QvBsinθF = BILsinθ

F/l = μ0I1I2/(2πr)τ = NIAB sinθ

QBr = mv

B = μ0I/(2πr)B = μ0NI/L

v = E/B

Φ = BAcosθ

( = -NΔΦ/Δt( = Blv

Vs/Vp = Ns/Np = Ip/Is

Electromagnetic Waves

c = 1/(ε0μ0)½

c =λf

u = ½ε0E2 + ½μ0 B2

= ε0E2 =μ0 B2

Geometric Optics

θinc = θrefl

f = r/2

1/do + 1/di = 1/f

m = hi/ho = -di/do

v = c/nλ = λ0/n

n1sinθ1 = n2sinθ2

sinθc = n2/n1

1/do + 1/di = 1/f

m = hi/ho = -di/do

Wave Properties of Light

dsinθ = mλ, m ’ 0, 1, 2, ...

dsinθ = (m + ½)λ, m ’ 0, 1, 2, ...

wsinθ = mλ, m ’ 1, 2, 3, ...

tan(θP) = n2/n1

I = Iocos2θ

Relativity

γ = 1/(1-v2/c2) ½

Δt = γ ΔtoL = Lo/γ

m = γmop = γmov

E = mc2 = γmoc2

E2 = p2c2 + mo2c4

KE = E - moc2 = (γ - 1)moc2

u = (v + u')/(1 + vu'/c2)

Modern Physics

λpT = 2.90 x 10-3 Km

E = nhfn = 1, 2, 3, …

E = hfp = E/c

hf = KEmax + W

KEmax = eVstop

W = hfcutoff

λ' = λ + h(1-cosφ)/ (moc)

λ = h/(mv)

L = mvrn = nh/(2π)n = 1, 2, 3, …

hf = Em – En

En = -13.6/n2 eV

rn = n2r1r1 = 0.529 x 10-10 m

Constants

g = 9.8 m/s2

G = 6.67 x 10-11 Nm2/kg2

c = 3 x 108 m/s

e = 1.6 x 10-19 C

k = 9 x 109 Nm2/C2

ε0 = 8.85 x 10-12 C2/Nm2

μ0 = 4π x 10-7 Tm/A

h = 6.63 x 10-34 Js

NA = 6.02 x 1023 mol-1

mp = 1.67 x 10-27 kg

me- = 9.11 x 10-31 kg

Simple Machines

AMA = Fout/Fin

TMA = din/dout

Efficiency = Workout / Workin

Efficiency = AMA/TMA

Rearth = 6.38 x 106 m

Mearth = 5.97 x 1024 kg

Msun = 1.99 x 1030 kg

Earth – sun distance = 1.50 x 1011 m

Earth – moon distance = 3.84 x 108 m...