Question

A uniform disc of radius $R=0.2m$ kept over a rough horizontal surface is given velocity ${\omega }_0$. After some time its kinetic energy becomes zero. If $v_0=10m/s$, find ${\omega }_0$.

Answer 1

K.E $=\frac{1}{2}m{v_0}^2-\frac{1}{2}I{w_0}^2$

$\Rightarrow 0=\frac{1}{2}m100-\frac{1}{2}\left(\frac{1}{2}m{r}^2\right){w_0}^2$

$0=50m-\frac{1}{4}m\left(0.04\right){w_0}^2$

$0=50m-0.01m{w_0}^2$

$50m=0.01m{w_0}^2$

${w_0}^2=5000$

$\Rightarrow w_0=70.71$ rad/s.

Hence, the answer is $70.71$ rad/s.