Question:
Suppose the platform with the kid in the previous problem is rotating in anticlockwise direction at an angular speed $w$. The kid starts walking along the rim with the speed $v$ relative to the platform also in the anticlockwise direction. Find the new angular speed of the platform.
Solution:
Let angular velocity of platform after kid start running $\omega^{\prime}$
So, angular velocity of kid with respect to earth $=\left(\omega^{\prime}+\frac{v}{R}\right)$ $\because \tau_{e x t}=0$
$\therefore L_{i}=L_{\omega}$
$\left(I+\mathrm{M} R^{2}\right) \omega=\mid \omega^{\prime}+\mathrm{MR}^{2}\left(\omega^{\prime}+\frac{v}{R}\right)$
$\omega^{\prime}=\omega-\frac{M v R}{T+M R^{3}}$