   Chapter 7, Problem 13P

Chapter
Section
Textbook Problem

A rotating wheel requires 3.00 s to rotate 37.0 revolutions. Its angular velocity at the end of the 3.00-s interval is 98.0 rad/s. What is the constant angular acceleration (in rad/s2) of the wheel?

To determine
The angular acceleration of the rotating wheel.

Explanation

Given info: The angular rotation is 37.0rev, the time is 30.0s , and the final angular velocity is 98.0rad/s , The initial angular velocity of the wheel is 57.0rad/s , the final angular velocity of the wheel is 98.0rad/s , and the time is 30.0s .

Explanation: The angular displacement of the wheel is equal to the product of the average angular velocity and the time taken to reach such an angular displacement. Rearrange this for the initial angular speed.

The formula for the initial angular velocity is,

ωi=2Δθtωf

• Δθ is the angular rotation of the wheel.
• t is the time for the wheel to reach the stated angular rotation.
• ωf is the final angular velocity of the wheel.

Substitute 37.0rev for Δθ , 30.0s for t , and 98.0rad/s for ωf to find ωf .

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