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 to . If the initial angular velocity is , what is the final angular velocity ? Well if the stool is frictionless, then the net torque on the person plus weights is zero, so angular momentum is conserved. So
So when the moment of inertia increases, the anglar velocity decreases.