Question

A wheel 1.00 m in radius is rotating at 100 rad/s. The wheel accelerates uniformly from 100 rad/s to 500 rad/s in 100 revolutions. Determine the rate of angular acceleration

Answer 1

The rate of angular acceleration can be determined using the equation: Angular acceleration (α) = (final angular velocity (ω) - initial angular velocity (ω0)) / time taken (t). Given that the initial angular velocity (ω0) is 100 rad/s, the final angular velocity (ω) is 500 rad/s, and the time taken (t) is 100 revolutions, we need to convert the time to seconds. By substituting the values into the equation and calculating, you can determine the rate of angular acceleration.

Step-by-step explanation:

The rate of angular acceleration can be determined using the equation:

Angular acceleration (α) = (final angular velocity (ω) - initial angular velocity (ω0)) / time taken (t)

Given that the initial angular velocity (ω0) is 100 rad/s, the final angular velocity (ω) is 500 rad/s, and the time taken (t) is 100 revolutions, we need to convert the time to seconds.

Since one revolution is equal to 2π radians, 100 revolutions is equal to 200π radians. Therefore, the time taken (t) is 200π seconds.

Substituting the values into the equation:

Angular acceleration (α) = (500 rad/s - 100 rad/s) / (200π s)

Calculating this value will give you the rate of angular acceleration.