Physics - Rotation Question with Solution | TestHub

The torque $\tau$ is related to the moment of inertia $I$ and angular acceleration $\alpha$ by $\tau =I\alpha$. Given $\tau =2.0\text{ N m}$ and $I=0.5{\text{ kg m}}^2$, the angular acceleration is $\alpha =\frac{\tau }{I}=\frac{2.0}{0.5}=4.0{\text{ rad/s}}^2$.

Using the rotational kinematic equation $\omega ={\omega }_0+\alpha t$, where $\omega =0$ (final angular speed), ${\omega }_0=20\text{ rad/s}$ (initial angular speed), and $\alpha =-4.0{\text{ rad/s}}^2$ (braking torque implies negative acceleration). So, $0=20-4.0t⟹4.0t=20⟹t=\frac{20}{4.0}=5.0\text{ s}$.