Why does an ice skater's angular velocity increase when she pulls in her arms during a spin?

An ice skater's angular velocity increases when she pulls in her arms because she reduces her moment of inertia. Moment of inertia is a measure of an object's resistance to changes in its rotation. It depends on how mass is distributed relative to the axis of rotation. When the skater pulls her arms closer to her body, she is effectively reducing the distance of her mass from the axis of rotation, which decreases her moment of inertia.

According to the principle of conservation of angular momentum, if no external torque acts on a system, the total angular momentum must remain constant. Angular momentum is the product of angular velocity and moment of inertia. Therefore, when her moment of inertia decreases (as she pulls her arms in), the angular velocity must increase to keep the angular momentum constant. This relationship is a key concept in rotational dynamics and explains why many athletes, including ice skaters, utilize this technique to spin faster.