I have a question regarding angular momentum and rot kinetic energy. For example, if angular momentum is conserved, and the radius is cut in half, then moment of inertia is reduced by a fourth, which will result in increase in angular velocity by factor of 4. My question is why is the rotational kinetic energy increase by a factor of 4 also. Since the equation of rot kinetic energy is (1/2)Iw^2, the new w increased by factor of 4 but the new I also decreased by factor of 1/4. So wouldn't KE stay the same???