If a particle with mass m moves with position vector r(t), then its angular momentum is defined as L(t) = mr(t) x v(t) and its torque as τ(t) = mr(t) x a(t).
Show that L'(t) = τ(t). Deduce that if τ(t) = 0 for all t, then L(t) is constant. (This is the law of conservation of angular momentum.)