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Conservation of angular momentum

If the net torque acting on a system is zero then


Which says that the total angular momentum is conserved. As with conservation of energy and conservation of momentum, this is a very useful law. Let's consider someone rotating around on a stool with nearly frictionless bearings.


If the person is holding some weights in their hands then they can change their moment of inertia by stretching out their hands. It increases from tex2html_wrap_inline860 to tex2html_wrap_inline862 . If the initial angular velocity is tex2html_wrap_inline864 , what is the final angular velocity tex2html_wrap_inline866 ? Well if the stool is frictionless, then the net torque on the person plus weights is zero, so angular momentum is conserved. So


and therefore


So when the moment of inertia increases, the anglar velocity decreases.

Joshua Deutsch
Sun Feb 23 15:54:50 PST 1997