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why is it harder for an ice skater to spin with his arms stuck out, as...

why is it harder for an ice skater to spin with his arms stuck out, as opposed to tucked in?

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Answer #1

when a When a figure skater draws her arms and a leg inward, she reduces the distance between the axis of rotation and some of her mass, reducing her moment of inertia. Since angular momentum is conserved, her rotational velocity must increase to compensate.

Now when her arms and a leg are out, they are further from her rotation axis. If her arms are straight out they have moment of inertia ½(2marm)r²arm, where rarm is the distance from the axis to her fingertips. If her leg is straight out, it contributes ½mlegr²leg. the skater's moment of inertia is much larger when her arms and one leg are out, all due to the r² dependence of I.

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