   Chapter 7.2, Problem 7.3QQ

Chapter
Section
Textbook Problem

Consider again the pairs of angular positions for the rigid object in Quick Quiz 7.1. If the object starts from rest at the initial angular position, moves counterclockwise with constant angular acceleration, and arrives at the final angular position with the same angular velocity in all three cases, for which choice is the angular acceleration the highest?

To determine
The highest angular acceleration.

Explanation

Given info: The time taken for the displacement is 1s .

Explanation:

The angular acceleration is given by,

α=ω2ω022Δθ

• ω is the final angular velocity
• ω0 is the initial angular velocity

Since the initial angular velocity is 0 ,

α=ω22Δθ

Since all the cases have equal final angular velocity, the option will have the lowest angular displacement will have the highest angular acceleration.

For option (a) Initial angular position is 3rad . Final angular position is 6rad

Angular displacement in option (a) is,

For option (b) Initial angular position is 1rad

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