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Chapter 10: Problem 2

A point on the rim of a rotating wheel has nonzero acceleration, since it's moving in a circular path. Does it necessarily follow that the wheel is undergoing angular acceleration?

Short Answer

Expert verified
No, it does not necessarily follow that the wheel is undergoing angular acceleration. Linear acceleration on a point on a rim of a wheel is present due to the centripetal force that keeps the point moving in a circular path. However, this does not imply that the wheel itself is undergoing angular acceleration.

Step by step solution

01

Understand the Terminologies

It is crucial to understand two kinds of accelerations with respect to a rotating body - Linear and Angular. Linear acceleration is the rate of change of linear speed. Angular acceleration is the rate of change of angular speed. A point on the rim of a rotating wheel is indeed undergoing linear acceleration because it is continually changing its direction.
02

Relate to Centripetal Acceleration

On recognizing that linear acceleration is present because it's moving in a circular path, we see that this is a case of centripetal acceleration - which is the acceleration of an object moving in a circular path. Despite a constant angular speed, the direction of the linear velocity vector changes constantly, indicating acceleration. This is however different from angular acceleration.
03

Define Angular Acceleration

Angular acceleration, on the other hand, refers to how quickly the angular velocity of an object is changing - meaning whether the rate of rotation is increasing or decreasing. This is a different concept from linear acceleration and is not necessarily present when linear acceleration exists.
04

Conclude the Analysis

Examining these principles in relation to one another, it can be concluded that the presence of linear acceleration on a point on the rim of a wheel does not inherently imply that the entire wheel is undergoing angular acceleration. Angular acceleration would only exist if the rate of rotation of the wheel was changing.

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Most popular questions from this chapter

A rolling ball has total kinetic energy \(100 \mathrm{J}, 40 \mathrm{J}\) of which is rotational energy. Is the ball solid or hollow?

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