Question

A solid disc of radius $20\, cm$ and mass $10\, kg$ is rotating with an angular velocity of $600\, rpm$, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in $10\, s$ is___ $\pi \times 10^{-1}Nm$

Answer 1

$\tau =\frac{\Delta L}{\Delta t}=\frac{I\left(\omega_{f}-\omega_{i}\right)}{\Delta t}$
$\tau =\frac{\frac{m R^{2}}{2} \times[0-\omega]}{\Delta t}$
$=\frac{10 \times\left(20 \times 10^{-2}\right)^{2}}{2} \times \frac{600 \times \pi}{30 \times 10} $
$=0.4 \pi=4 \pi \times 10^{-2}$