Question

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

Answer 1

Considering bottom most print $V_p:V_0+r{w}_0$

If disc steps both $v$ & $w$ becomes zero

Angular momentum about $P$ is conserved

$v_0=10r=0.2$

$\therefore w_0=\frac{2v_0}{r}$

$=\frac{2\times 10}{0.2}=100$

$L_1=m{v}_{0}r-I_0{w}_0=L_{final}=0$

$m{v}_{0}r=I_0{w}_0=1$

$m{v}_{0}r=\frac{m{v}^2}{2}.w_0$

$2v_0=r{w}_0$