Question

A uniform circular disc of radius $r$ is placed on a rough horizontal surface and given, a linear velocity $v_0$ and angular velcoity ${\omega }_0$ as shown. The disc comes to rest after moving some distance to right. It follows that

• A. $3v_0=2{\omega }_{0}r$
• B. $2v_0={\omega }_{0}r$
• C. $v_0={\omega }_{0}r$
• D. $2v_0=3{\omega }_{0}r$

Answer 1

The correct option is B $2v_0={\omega }_{0}r$

According to conservation of angular momentum
if ${\tau }_{\text{ext}}=0$, then $L=$ constant

We can write
$\therefore L_{\text{initial}}=L_{\text{final}}$

Putting values
$m{v}_{0}r-I_0{\omega }_0=0$

After solving
$m{v}_{0}r=\frac{1}{2}m{r}^2{\omega }_0\Rightarrow 2v_0={\omega }_{0}r$

Hence the relation is as given above