Question

A solid disc of radius $20cm$ and mass $10kg$ is rotating with an angular velocity of $600rpm$, 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 $10s$ is___ $\pi \times 10^{-1}Nm$

Answer 1

Answer: 4

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