What happens to the speed of a spinning object if its radius decreases while maintaining its angular momentum?

When an object's radius decreases while maintaining its angular momentum, the speed of the object must increase. Angular momentum is defined as the product of the moment of inertia and the angular velocity (speed). The moment of inertia is directly related to the radius; as the radius decreases, the moment of inertia also decreases.

To maintain a constant angular momentum, if the moment of inertia decreases, the angular velocity (or speed) must increase to compensate for that decrease. This relationship can be expressed by the formula for angular momentum:

[ L = I \cdot \omega ]

where ( L ) is the angular momentum, ( I ) is the moment of inertia, and ( \omega ) is the angular velocity. Thus, if the radius decreases, leading to a lower moment of inertia, the angular velocity must increase to keep the angular momentum constant, confirming that speed increases as radius decreases in this context.