Formulas 2

Momentum and impulse

p= mv,   F = p /∆t,  I = ∆p = F∆t.
Center of mass:  xCM = ∑mixi/M,  yCM = ∑miyi/M,  zCM = ∑mizi/M,  M = ∑mi.

Rotations

ωavg = (θf - θi)/(tf - ti) = Δθ/Δt.
ωf = ωi + α(tf - ti),  θ= θi + ωi(tf – ti) + ½α(tf – ti)2
τ = r × F = Iα = ΔL/Δt,  L = Iω.
Moment of inertia:  I = ∑miri2.
Rolling:  KEtot = ½mv2 + ½Iω2,  v = rω.

Ideal Fluids

Equation of continuity:  A1v1 = A2v2
Bernoulli’s equation:  P1 + ρgh1 + ½ρv12 = P2 + ρgh2 + ½ρv22

Viscous fluids

Poiseuille’s law: Q = π∆Pr4/(8ηL)
Stokes' law: F = 6πηrv
Reynolds number:  R = ρDv/η
Surface tension, Laplace's law for a spherical membrane:  Pi - Po = 2γ/r.
Capillary action:  h = 2γcosθ/(ρgr).