Physics - Rotation Question with Solution | TestHub

Initial angular velocity is ${\omega }_0=240\text{ r.p.m.}=240\times \frac{2\pi }{60}=8\pi \text{ rad/s}$.

Final angular velocity is $\omega =0$.

Time taken to come to rest is $t=20\text{ s}$.

Angular retardation is given by $\alpha =\frac{{\omega }_0-\omega }{t}=\frac{8\pi -0}{20}=\frac{2\pi }{5}{\text{ rad/s}}^2$.

Moment of inertia of the disc is $I=\frac{1}{2}M{R}^2=\frac{1}{2}\times 25\times (0.2{)}^2=0.5{\text{ kg m}}^2$.

Retarding torque is $\tau =I\alpha =0.5\times \frac{2\pi }{5}=\frac{\pi }{5}\text{ N m}$.

Since the torque is due to a tangential force $F$ on the rim, $\tau =F\times R$.

Therefore, $F=\frac{\tau }{R}=\frac{\pi /5}{0.2}=\pi \text{ N}$.

Answer: $\pi \mathrm{N}$