What happens to the angular velocity of a rotating object when its moment of inertia decreases?

When the moment of inertia of a rotating object decreases, the angular velocity of that object increases due to the principles of angular momentum conservation. Angular momentum is defined as the product of the moment of inertia and the angular velocity. For a closed system with no external torques acting upon it, the angular momentum remains constant.

Mathematically, this relationship is represented as:

Angular Momentum (L) = Moment of Inertia (I) × Angular Velocity (ω)

If there is a change in the moment of inertia (I), and angular momentum (L) must remain constant, then an increase in angular velocity (ω) occurs if the moment of inertia decreases. This inverse relationship means that as the moment of inertia reduces, the angular velocity compensates by increasing to keep the angular momentum constant.

For example, consider a figure skater who pulls in their arms while spinning. As the moment of inertia decreases (due to the arms being closer to the center of rotation), the skater spins faster, demonstrating this principle in action. Thus, the decrease in moment of inertia leads directly to an increase in angular velocity.