Question

An engine flywheel initially rotates counterclockwise at 5.03 rotations/s. Then, during 23.5 s, its rotation rate changes to 2.63 rotations/s clockwise. Find the flywheel's average angular acceleration (including its sign) in radians per second squared. Define counterclockwise rotation as positive.

Answer 1

Answer:

the flywheel's average angular acceleration is -2.05 rad/s²

Explanation:

Note: counterclockwise is positive

         clockwise is negative

Given;

initial angular velocity, $\omega _i$ = 5.03 rev/s = $5.03\frac{rev}{s} \times \frac{2\pi \ rad}{1 \ rev} = 31.61 \ rad/s$

final angular velocity, $\omega_f$= -2.63 rev/s = $-2.63 \ \frac{rev}{s} \times \frac{2\pi \ rad}{1 \ rev} = -16.53 \ rad/s$

duration of the flywheel rotation, Δt = 23.5 s

The average acceleration of the flywheel is calculated as;

$a_r = \frac{\Delta \omega}{\Delta t} = \frac{\omega_f - \omega _i}{t_2-t_1} = \frac{-16.53 \ - \ 31.61}{23.5} = -2.05 \ rad/s^2$

Therefore, the flywheel's average angular acceleration is -2.05 rad/s²