Proof of Conservation of Angular Momentum
Angular momentum is conserved for a body subject to no net external torque.
Let a body consist of particlesat position vectors
The motion of each particle is determined by Newton's second lawor
Taking the cross product withand summing overgives
We can write
The right hand side of this equation is the rate of change of angular momentum. Consider
by Newton's third law so ifthenand angular momentum is conserved.