A rotating ice skater starts with her arms extended and then pulls them close to her body. Determine whether her angular velocity increases, decreases, or remains the same, assuming angular momentum is conserved.
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If angular momentum is conserved, the product of the moment of inertia and angular velocity must remain constant.
When the ice skater pulls her arms close to her body, her moment of inertia decreases. This is because the moment of inertia depends on the distribution of mass from the axis of rotation - when the mass is closer to the axis, the moment of inertia decreases.
If the moment of inertia decreases, in order for the product of the moment of inertia and angular velocity to remain constant, the angular velocity must increase. Therefore, the ice skater's angular velocity increases when she pulls her arms close to her body.
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