Britannica Sources used in this answer

Why does a spinning ice skater rotate faster after pulling in their arms?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A. — mechanics Figure 1: (A) The vector sum C = A + B = B + A. (B) The vector difference A + (−B) = A − B = D. (C, left) A cos θ is the component of A along B and (right) B cos θ is the component of B along A. (D, left) The right-hand rule used to find the direction of E = A × B and (right) the right-hand rule used to find the direction of −E = B × A.

A spinning ice skater rotates faster after pulling in their arms due to the law of conservation of angular momentum. This principle states that for a system isolated from external torque, the total angular momentum remains constant.12

Angular momentum ( $L$ ) is defined as the product of the moment of inertia ( $I$ ) and the angular velocity ( $ω$ ), expressed as $L = I ω$ . The moment of inertia is a measure of an object's resistance to changes in its rotation and depends on the distribution of mass relative to the axis of rotation.23

When a skater pulls their arms inward, they decrease their moment of inertia ( $I$ ) by bringing mass closer to the axis of rotation. Because the total angular momentum ( $L$ ) must remain constant, the angular velocity ( $ω$ ) must increase to compensate for the reduction in $I$ . Consequently, the skater spins faster.2