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Chapter 11: Problem 6

A group of polar bears is standing around the edge of a slowly rotating ice floe. If the bears all walk to the center, what happens to the rotation rate?

Short Answer

Expert verified
The rotation rate of the ice floe increases when the polar bears walk towards the center due to the conservation of angular momentum.

Step by step solution

01

Identifying the Concept

The problem centers around the concept of rotational motion - specifically the principle of conservation of angular momentum. This principle states that if no external torque acts on a system, then the total angular momentum of the system remains constant.
02

Understanding the Situation

In the given problem, the 'system' in question consists of the group of polar bears and the ice floe. Initially, the bears are located around the edge of the floe. This means that they are far from the axis of rotation, contributing to a larger moment of inertia for the system, causing a slow rotation rate of the floe.
03

Applying Angular Momentum Conservation

As the polar bears move to the center, their distance from the axis of rotation decreases, thereby lowering the moment of inertia of the system. However, since no external torque acts on the system, the total angular momentum must remain conserved. Therefore, decrease in moment of inertia is accompanied by an increase in angular speed to keep the product of moment of inertia and angular speed constant.
04

Interpreting the Result

The increase in angular speed caused by the movement of the bears towards the center of the floe implies an increase in the rotation rate of the ice floe. Thus, as the polar bears move to the center, the rotation rate of the ice floe increases.

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Most popular questions from this chapter

Does a particle moving at constant speed in a straight line have angular momentum about a point on the line? About a point not on the line? In either case, is its angular momentum constant?

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