Where does the increase in kinetic energy come from when an ice skater pulls in her arms?

When an ice skater pulls in her arms, the increase in kinetic energy is primarily a result of the conservation of angular momentum. As the skater reduces her radius by pulling in her arms, her moment of inertia decreases. To conserve angular momentum (which remains constant when no external torques are acting on the system), her angular velocity must increase. This results in a higher rotational speed, which correlates to an increase in kinetic energy.

Mechanical energy is the sum of potential and kinetic energy in a system. Although the skater’s action involves mechanical energy, the specific source of the increase in kinetic energy during the movement does not stem from mechanical energy itself but rather from the skater's own motion and the adjustments she makes to maintain angular momentum.

Electrical energy and nuclear energy do not apply to the context of the skater's motion; these forms of energy are not involved in the physical actions of an ice skater. Chemical energy is related to reactions in chemical substances and is not the energy source being transformed in this scenario. The correct reasoning reveals that the change in kinetic energy is fundamentally linked to the skater's adaptation of her position to maintain rotational stability while increasing her speed, showcasing the principles of physics at work.