Final answer:
When the moment of inertia decreases, the kinetic energy increases. This is due to the direct proportionality between kinetic energy, moment of inertia, and square of angular velocity.
Step-by-step explanation:
When the moment of inertia of an object decreases, its kinetic energy increases. This is because kinetic energy is directly proportional to both the moment of inertia and the square of the angular velocity.
For example, consider a skater pulling her arms inward. As her moment of inertia decreases, the work required to pull her arms inward increases, resulting in an increase in her rotational kinetic energy. However, her angular momentum remains constant.
It's important to note that in a frictionless environment, no energy is lost from the system. Therefore, if the skater were to extend her arms back to their original positions, her kinetic energy would return to its original value.