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When the external torque acting on a rotating object is zero, its angular momentum is conserved. For a rotating object the angular momentum can be expressed as the product of rotational inertia and angular velocity. This gives an equation that is useful in problem solving. However, when using this equation there is no clue as to what is happening to the energy of the system. When introduced to the topic of conservation of angular momentum, students ask questions about the conservation of energy and kinetic energy. However, there is neither a textbook nor article in physics teaching journals that would address the issue of energy for cases where the angular momentum is conserved. The answers to questions of students are given here.