The angular momentum L(t) and torque(t) of a moving particle of mass m with position vector r(t) are defined to be:

L(t) = mr(t) v(t) and(t) = mr(t) a(t)

a/ Prove that L'(t) =(t)

b/ Prove that if(t) 0, then L(t) must be a constant vector. (this is the law of conservation of angular momentum).