Physics Equations

Kinematics / Projectiles

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 = ma Fgravity = mg

Ffriction ≤ μsN Ffriction = μkN

Circular Motion

Fnet = mv2/r ac = v2/r

v = 2πr/T

f = 1/T T = 1/f

Gravitation

F = GM1M2/R2 g = GM/R2

T2/R3 = 4π2/GM = constant

GM = Rv2
Energy

W = Fdcosθ KE = ½mv2

PE = mgh PE = 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 ’ ?ωt ω = (ωo + ω)/2

ω ’ ωο + αt θ ’ ωοt + ½αt2

ω2 ’ ωο2 + 2αθ

s = rθ v = r ω atan = rα

τ = r x F

Ι ’ Σmr2 Ιparallel = ICM + md2

Στ ’ Ια L ’ Ιω

Στ ’ dL/dt L = r x p

ΚΕ ’ ½Ιω2

Bodies in Equilibrium

Στ ’ 0 ΣF ’ 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/2L λ1 = 2L fn = nf1 λn = λ1/n n = 1, 2, 3, …..

Sound

β ’ 10log(1012Ι)

vsound = 331 + .6T(0C)

f = f0(v±v0)/(v±vs)

f1 = v/2L λ1 = 2L fn = nf1 λn = λ1/n n = 1, 2, 3, …..

f1 = v/4L λ1 = 4L fn = nf1 λn = λ1/n n = 1, 3, 5, ….

fB = │f1 – f2│

sinθ = vsound / vobject

Electrostatics

F = QE F = kQ1Q2/r2

E = kQ/r2

ΔPE = QΔV PE = kQ1Q2/r

V = kQ/r ΔV = EΔx

C= Q/V C = ε0A/d

C = κC0 E = Q/(ε0A)

U = ½QV = ½CV2 =½Q2/C

u= ½ε0E2