Kinematic equations for one-dimensional motion with constant acceleration

a_x = (v_xf - v_xi)/∆t, where ∆t = (t_f - t_i).
v_xf = v_xi + a_x ∆t.
v_x(avg) = (v_xf + v_xi)/2.
x_f - x_i = v_xi∆t + ½ a_x∆t².
v_xf² = v_xi² + 2a_x(x_f - x_i).

Projectile motion

v_x = v_0x,  ∆x = v_0xt,  v_y = v_0y - gt,  y = y₀ + v_0yt - ½ gt².

Hooke's law

F = -kx

Work, energy and power

W = F·d ,
The work done by a force can be positive or negative.  If the component of the force in the direction of the displacement is positive, the work is positive, and if the component of the force in the direction of the displacement is negative, the work is negative.
Kinetic energy: K = ½mv².
Gravitational potential energy: U_g = mgh (with ground as reference).
Elastic potential energy: U_s = ½ kx².
P = ∆W/∆t

Friction

f_s≤ μ_sN, f_k = μ_kN.

Uniform circular motion:

Centripetal acceleration: a_c = v²/r.
Centripetal force: F_c = mv²/r.

Momentum and impulse

p = mv,   F = ∆p /∆t,  I = ∆p = F∆t.
Center of mass:  x_CM = ∑m_ix_i/M,  y_CM = ∑m_iy_i/M,  z_CM = ∑m_iz_i/M,  M = ∑m_i.

Rotations

ω_avg = (θ_f - θ_i)/(t_f - t_i) = Δθ/Δt.
ω_f = ω_i + α(t_f - t_i),  θ_f = θ_i + ω_i(t_f - t_i) + ½α(t_f - t_i)², 
τ = r × F = Iα = ΔL/Δt,  L = Iω.
Moment of inertia:  I = ∑m_ir_i².
Rolling:  KE_tot = ½mv² + ½Iω²,  v = rω.