An ice skater performs a fast spin by pulling outstretched arms down and close to her body. What happens to her angular momentum with respect to the axis of rotation?

Question

BlackTom AI · Accepted Answer

Consider the scenario: an ice skater spins about a vertical axis and pulls her arms in. The key concept is angular momentum conservation: in the absence of external torques, the total angular momentum L = Iω remains constant.
Option 1: 'It doesn’t change' — This aligns with the conservation of angular momentum. When she pulls her arms in, her moment of inertia I decreases, so her angular velocity ω must increase accordingly to keep L constant. The overall angular momentum about the axis remains the same.
Option 2: 'It depends how fast she rotates' — The angular momentum does not depend on how fast she starts spinning in this sense; regardless of initial speed, if external torque is negligible, L is conserved. The rotation speed changes, but L stays the same.
Option 3: 'It decreases' — This would imply a loss of angular momentum, which would require an external torque. In a frictionless, isolated system (idealized ice rink with no external torques), there is no mechanism for L to decrease simply by bringing in the arms.
Option 4: 'It increases' — This would violate conservation of angular momentum unless an external torque or an external agent contributes angular momentum to the system. Merely changing the distribution of mass internally does not create net angular momentum.
In summary, only the first option correctly describes the expectation given angular momentum conservation during a change in the skater’s moment of inertia.

An ice skater performs a fast spin by pulling outstretched arms down and close to her body. What happens to her angular momentum with respect to the axis of rotation? Single choice

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