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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 doesn't necessarily follow that a wheel is undergoing angular acceleration just because a point on its rim is undergoing linear acceleration. The wheel undergoes angular acceleration only if its angular velocity (speed of rotation) changes.

Step by step solution

01

Understanding linear and angular acceleration

The first step is to understand linear and angular acceleration. Linear acceleration is the change in linear speed or direction, while angular acceleration is the rate at which angular velocity changes with respect to time. If a point is moving in a circular path, it is definitely undergoing linear acceleration because its direction of motion is continually changing. However, it would only be undergoing angular acceleration if the rate of rotation of the wheel was changing.
02

Identify the relationship between linear and angular acceleration

In the case of a point on the rim of a wheel, the point exhibits linear (tangential) acceleration if the angular velocity of the wheel is changing - i.e., the wheel exhibits angular acceleration. Centripetal or radial acceleration (towards the center) does not affect the angular acceleration, it is a consequence of circular motion at a constant speed.
03

Make the conclusion

With the above understanding, just because a point on the rim of a wheel exhibits linear acceleration due to circular motion, it does not imply that the wheel is undergoing angular acceleration. The wheel undergoes angular acceleration only if its angular speed is changing.

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