A circular platform is mounted on a frictionless vertical axle. Its radius $R=2 \mathrm{~m}$ and its moment…
A circular platform is mounted on a frictionless vertical axle. Its radius $R=2 \mathrm{~m}$ and its moment of inertia about the axle is $200 \mathrm{~kg} \mathrm{~m}^2$. It is initially at rest. A $50 \mathrm{~kg}$ man stands on the edge of the platform and begins to walk along the edge at the speed of $1 \mathrm{~ms}^{-1}$ relative to the ground. Time taken by the man to complete one revolution is
$\pi \sec$
$\frac{3 \pi}{2} \sec$
$2 \pi \mathrm{sec}$
$\frac{\pi}{2} \sec$
Solution
From conservation of angular momentum
$\begin{aligned}
I \omega & =m v r \\
200 \times \omega & =50 \times 2 \times 1 \\
\omega & =\frac{1}{2} \mathrm{rad} / \mathrm{s}
\end{aligned}$
$\begin{aligned}
\quad v & =r \omega=1 \mathrm{~m} / \mathrm{s} \\
\therefore \quad T & =\frac{2 \pi r}{1-(-1)}=\frac{2 \pi r}{2}=\pi r=2 \pi \mathrm{s}
\end{aligned}$