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

Answer:

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

Explanation:

Given;

initial angular distance, θ = 28

time of the motion, t = 5 s

initial angular velocity is calculated as;

$\omega _i = \frac{\theta}{t} = \frac{28}{5}.\frac{rev}{s} \ \times \ \ \frac{2 \pi \ rad}{1 \ \ rev} = 35.19 \ rad/s$

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

The constant angular acceleration is calculated as;

$\alpha = \frac{\omega _f - \omega _i}{t} \\\\\alpha = \frac{96 - 35.19}{5} \\\\\alpha = 12.16 \ rad/s^2$

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