(II) A figure skater can increase her spin rotation rate...

(II) A figure skater can increase her spin rotation rate from an initial rate of 1.0 rev every 2.0 $\mathrm{s}$ to a final rate of 3.0 $\mathrm{rev} / \mathrm{s}$ . If her initial moment of inertia was 4.6 $\mathrm{kg} \cdot \mathrm{m}^{2}$ , what is her final moment of inertia? How does she physically accomplish this change?

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Key Concepts

Conservation of Angular Momentum

This principle states that in the absence of external torques, the angular momentum of a system remains constant. It implies that any change in the moment of inertia will result in an inverse change in angular velocity to keep the product of the two constant. In rotational systems like a spinning skater, pulling arms inward reduces the moment of inertia, leading to an increase in spin rate.

Moment of Inertia

Moment of inertia is a measure of how mass is distributed relative to the axis of rotation, determining how resistant an object is to angular acceleration. When a figure skater pulls her arms closer to her body, the mass distribution becomes tighter around the axis, reducing her moment of inertia and allowing her to spin faster.

Angular Velocity

Angular velocity describes the rate at which an object rotates and is typically measured in revolutions per second or radians per second. Under the conservation of angular momentum, a decrease in moment of inertia causes an increase in angular velocity, as observed when a figure skater speeds up her rotation by altering her body shape.

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