Question

A rotating wheel requires 5.00 s to rotate 28.0 revolutions. Its angular velocity at the end of the 5.00-s interval is 96.0 rad/s. What is the constant angular acceleration (in rad/s) of the wheel

Answer 1

The constant angular acceleration of the wheel is 12.16 rad/s²

Step-by-step explanation:

Given;

initial angular distance, θ = 28

time of the motion, t = 5 s

initial angular velocity is calculated as;

`\omega _i = (\theta)/(t) = (28)/(5).(rev)/(s) \ * \ \ (2 \pi \ rad)/(1 \ \ rev) = 35.19 \ rad/s`

final angular velocity is given as,
`\omega _f = 96.0 \ rad/s`

The constant angular acceleration is calculated as;

`\alpha = (\omega _f - \omega _i)/(t) \\\\\alpha = (96 - 35.19)/(5) \\\\\alpha = 12.16 \ rad/s^2`

Therefore, the constant angular acceleration of the wheel is 12.16 rad/s²