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.

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