A diver (such as the one shown in Fig. 11-2 ) can reduce her...

A diver (such as the one shown in Fig. $11-2$ ) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in $1.5 \mathrm{~s}$ when in the tuck position, what is her angular speed (rev/s) when in the straight position?

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Key Concepts

Conservation of Angular Momentum

This fundamental principle states that in the absence of external torques, the initial angular momentum of a system equals its final angular momentum. In rotational dynamics, if a diver changes her moment of inertia—such as by tucking or straightening her body—her angular velocity adjusts to conserve angular momentum. This is the key concept that explains why a change in body configuration can significantly alter her rotation speed.

Moment of Inertia

The moment of inertia is a measure of an object's resistance to changes in its rotational motion and depends on the mass distribution relative to the axis of rotation. In the context of diving, changing body positions (from tuck to straight) affects the moment of inertia, and subsequently, the rotational speed, since a larger moment of inertia results in a slower angular velocity when angular momentum is conserved.

Angular Velocity

Angular velocity quantifies the rate of rotation and is typically expressed in revolutions per second or radians per second. It is directly impacted by changes in the moment of inertia, as described by the conservation of angular momentum. Understanding how to compute and convert angular velocity is essential in analyzing rotations in dynamical systems such as human dives.

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