Solve the following :

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 $=\left(\omega^{\prime}+\frac{v}{R}\right)$ $\because \tau_{e x t}=0$

$\therefore L_{i}=L_{\omega}$

$\left(I+\mathrm{M} R^{2}\right) \omega=\mid \omega^{\prime}+\mathrm{MR}^{2}\left(\omega^{\prime}+\frac{v}{R}\right)$

$\omega^{\prime}=\omega-\frac{M v R}{T+M R^{3}}$

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