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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A rigid body is rotating counterclockwise about a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid body. Which of the sets can occur only if the rigid body rotates through more than 180°? (a) 3 rad, 6 rad; (b) −1 rad, 1 rad; (c) 1 rad, 5 rad.

To determine

Whether the rigid body rotates more than 180° for the required angular displacement.

Explanation

For the rigid body to rotate more than 180° the angular displacement must be more than 3.14rad.

Conclusion:

Angular displacement for (c) is,

Δθ=5rad1rad=4rad

The angular displacement is more than 3.14rad. Hence, the rigid body does not rotate more than 180°. Therefore, option (c) is correct.

Angular displacement for (a) is,

Δθ=6rad3rad=3rad

The angular displacement is less than 3

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