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Chapter 11: Problem 8

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
If all the polar bears move towards the center, the rotation rate of the ice floe increases.

Step by step solution

01

Understand the Concept of Angular Momentum

Angular momentum can be represented using the formula \(L = I\omega\), where \(L\) is the angular momentum, \(I\) is the moment of inertia, and \(\omega\) is the angular velocity. Moment of inertia is defined as \(I = mr^2\), where \(m\) is the mass and \(r\) is the distance to the axis of rotation.
02

Apply Principle of Conservation of Angular Momentum

The principle of conservation of angular momentum states that, in the absence of external torques, the angular momentum of a system remains constant. As the polar bears move from the edge to the center (reducing the \(r\) in the moment of inertia), the product \(I\omega\) must remain constant. Therefore, as \(I\) decreases, \(\omega\) must increase to compensate.
03

Interpret the Result

In this context, \(\omega\) is the rotation rate of the ice floe. So, as the polar bears move towards the center, the rotation rate of the ice floe increases - meaning it spins faster.

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