Kinematics
 

v = v0 + at	Δx = ½(v0 + vf)t = vavet	Δx = v0t + ½at2
ω = ω0 + αt	Δθ = ½(ω0 + ωf)t = ωavet	Δθ = ω0t + ½αt2

 

Tangential — Rotational
 

ΔS = rΔθ

vtangential = rω

atangential = rα

 

Rolling
 

ΔS = Δx

atangential = alinear

 

Newton?s Laws
 
 

Torque
 

τ = Iα

τ = r × F

τz = rFperpendicular = rFsinφ = xFy − yFx

 

_{Moment of Inertia}
 

Itotal = I1 + I2 + I3 + …

I = ICM + Md2

 

Work and Energy
 

Wnc = ΔK + ΔU	W = FΔxcos(φ)	Klinear = ½mv2
Krotational = ½Iω2	Ugravity = mgh	Uspring = ½Kx2

 

Collisions
 

p = mv

Pf = Pi

v1f − v2f = − (v1i − v2i)

I =ΔP =Faveraget

 

Angular Momentum
 

L = r × p	Lz = xpy − ypx = rpsinφ		Lfinal = Linitial
Ltotal = L1 + L2 + ?	Llinear = bmv	Lorbital = r2mω		LA = IAωA

 

Simple Harmonic Motion
 

x(t) = Acos(ωt + δ)	v(t) = −ωAsin(ωt + δ)	a(t) =  −ω2Acos(ωt + δ)

 

 Waves
 
 

Standing Waves
 
 

If the string is fixed at both ends or air column is open at both ends

Use

Use
 
 

If the string or air column has one open end and one fixed end

Use

Use
 

yn(x,t) = Ancos(ωnt)sin(knt)

ωn = 2πfn

 

Sound Level / Decibels / Sound Intensity
 

Itotal = I1 + I2 + I3 + ?
Itotal = I0× 10(β/10)	I0 = 1 × 10-12 W/m2

 

Doppler Shift

Use