(II) A diver (such as the one shown in Fig. 2) can reduce...

(II) A diver (such as the one shown in Fig. 2$)$ can reduce her moment of inertia by a factor of about 35 when changing from the straight position to the tuck position. If she makes 20 rotations in 1.5 $\mathrm{s}$ when in the tuck position, what is her angular spced (rev/s) when in the straight position?

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Key Concepts

Rotational Kinematics

Rotational kinematics involves the analysis of rotation in terms of angular displacement, angular velocity, and angular acceleration. It provides relationships between these variables allowing the prediction of changes in rotational motion following alterations in the moment of inertia.

Angular Velocity

Angular velocity quantifies the rate of rotation, typically expressed in revolutions per second or radians per second. It is inversely related to the moment of inertia in a system where angular momentum is conserved.

Conservation of Angular Momentum

This principle states that if no external torque acts on a system, its total angular momentum remains constant. In rotational systems, a change in the moment of inertia must be compensated by an opposite change in angular velocity to preserve the overall angular momentum.

Moment of Inertia

The moment of inertia is a measure of an object’s resistance to changes in its rotational motion, depending on the mass distribution relative to the axis of rotation. Altering body positions, such as tucking in a diver’s limbs, significantly changes the moment of inertia.

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