Why does an ice skater spin faster when she folds her arms close to her body?

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The question asks: Why does an ice skater spin faster when she folds her arms close to her body?
Option a: Her moment of inertia is constant while her angular momentum is smaller. This is inconsistent with angular momentum conservation in a no-torque scenario; folding arms reduces the radius, which decreases the moment of inertia, not keeps it constant, and angular momentum does not become smaller automatically. So this is incorrect.
Option b: Her moment of inertia is constant while her angular momentum is larger. Keeping the moment of inertia constant while speeding up rotation would require an external torque to increase angular momentum; in a typical ice-skater scenario there is no such external torque, so this is false.
Option c: Her moment of inertia is larger while her angular momentum is constant. Increasing the moment of inertia would slow down rotation if angular momentum were conserved, which contradicts the observed speeding up when arms are folded. Therefore this choice is incorrect.
Option d: Her moment of inertia is smaller while her angular momentum is constant. This aligns with the conservation of angular momentum: when the skater reduces her radius by pulling in her arms, I decreases; since angular momentum L = I ω stays constant in the absence of external torque, the angular velocity ω must increase, making her spin faster. This accurately captures the physics of the scenario.
In summary, the key idea is the inverse relationship between moment of inertia and angular speed under angular momentum conservation: folding arms lowers I, so ω must rise to keep L constant. The other options either violate the conservation principle or misstate how I and L change together during the maneuver.

UCIC 202503 PHYS101 Quiz 5

Why does an ice skater spin faster when she folds her arms close to her body?

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