Answer
The flywheel turns through an angle of $~~20.4~rad$
Work Step by Step
We can find the initial angular velocity:
$L_i = I\omega_i$
$\omega_i = \frac{L_i}{I}$
$\omega_i = \frac{3.00~kg~m^2/s}{0.140~kg~m^2}$
$\omega_i = 21.429~rad/s$
We can find the final angular velocity:
$L_f = I\omega_f$
$\omega_f = \frac{L_f}{I}$
$\omega_f = \frac{0.800~kg~m^2/s}{0.140~kg~m^2}$
$\omega_f = 5.714~rad/s$
We can find the average angular velocity:
$\omega_{ave} = \frac{\omega_i+\omega_f}{2}$
$\omega_{ave} = \frac{21.429~rad/s+5.714~rad/s}{2}$
$\omega_{ave} = 13.57~rad/s$
We can find the angle through which the flywheel turns:
$\theta = \omega_{ave}~t$
$\theta = (13.57~rad/s)(1.50~s)$
$\theta = 20.4~rad$
The flywheel turns through an angle of $~~20.4~rad$
