Formulas 2

Friction and drag

Friction:  fs ≤ μsN,  fk= μkN
Uniform circular motion:  F = mv2/r

Work and energy

Work:  W = F·d
Scalar product:  A·B = ABcosθ = AxBx + AyBy + AzBz

Hooke's law:  F = -kr,  Fx= -kx
Elastic potential energy:  W = (1/2)kx2
Conservative systems:  E = K + U,  Fx = -dU/dx

Work-kinetic energy theorem:  Wnet = ∆K = (1/2)m(vf2 - vi2)
Power:  P = F·v  or  P = ∆W/∆t
coefficient of restitution:  (outgoing speed)/(incoming speed)

Gravitational force:  F12 = (-G m1m2/r122) (r12/r12)
Gravitational potential energy:  Uf - Ui = -G m1m2(1/r12f - 1/r12i)

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.