Question

A rotating wheel requires 8.00 s to rotate 27.0 revolutions. Its angular velocity at the end of the 8.00-s interval is 99.0 rad/s. What is the constant angular acceleration (in rad/s) of the wheel?

Answer 1

The constant angular acceleration of the wheel is 12.375 rad/s².

Step-by-step explanation:

Given that the rotating wheel requires 8.00 s to rotate 27.0 revolutions and its angular velocity at the end of the 8.00-s interval is 99.0 rad/s, we can determine the constant angular acceleration of the wheel using the formula:

Angular velocity (final) = Angular velocity (initial) + (Angular acceleration * Time)

Let's assume the initial angular velocity is 0 rad/s, since the wheel starts from rest. Plugging in the given values, we get:

99.0 rad/s = 0 rad/s + (Angular acceleration * 8.00 s)

Simplifying the equation, we find that the constant angular acceleration of the wheel is 12.375 rad/s².