Question

prove that the rate of change of angular momentum is equal to the torque acting on it
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Answer 1

Answer:

Theorem: The rate of change of the total angular momentum of a system of particles is equal to the sum of the external torques on the system. But the first term is zero, because ˙r and pi are parallel. But ∑i∑jFij=0 by Newton's third law of motion, and so ∑i∑jri×Fij=0.

Answer 2

Answer:

Theorem: The rate of change of the total angular momentum of a system of particles is equal to the sum of the external torques on the system. But the first term is zero, because ˙r and pi are parallel. But ∑i∑jFij=0 by Newton's third law of motion, and so ∑i∑jri×Fij=0.