Why does a spinning ice skater's angular velocity increase as she brings her arms in toward her body?

A spinning ice skater illustrates the principle of conservation of angular momentum, which states that if no external torques act on a system, the total angular momentum remains constant. When the skater brings her arms in toward her body, several interconnected factors come into play.

First, as the skater pulls her arms in, her mass moment of inertia decreases. The moment of inertia is a measure of how mass is distributed relative to an axis of rotation. When the mass is closer to the axis (which happens when she brings her arms in), the moment of inertia becomes smaller.

Since angular momentum is defined as the product of moment of inertia and angular velocity (L = Iω), and with angular momentum conserved, a reduction in moment of inertia must lead to an increase in angular velocity. This is known as the conservation of angular momentum.

Furthermore, the radius of gyration is also reduced as the skater's arms are drawn in. The radius of gyration refers to an effective distance from the axis of rotation where the mass can be assumed to be concentrated. When the arms are close to the body, this effective distance shortens, which corresponds with the decrease in moment of inertia.

Therefore, bringing her arms in not only reduces her mass moment