Angular Momentum in Case of Rotation about a Fixed Axis

A man stand on a rotating platform with his arms stretched is holding a $5 \mathrm{kg}$ weight in each hand. The angular speed of the platform is $1.2 \mathrm{rev} {\mathrm{s}}^{-1}$. The moment of inertia of the man together with the platform may be taken to be constant and equal to $6 \mathrm{kg} {\mathrm{m}}^2$. If the man brings his arms close to his chest with the distance of each weight from the axis changing from $100 \mathrm{cm}$ to $20 \mathrm{cm}$, the new angular speed of the platform is

Two bodies have moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio of

A solid cylinder of mass $20 \mathrm{k}\mathrm{g}$ and radius $20 \mathrm{c}\mathrm{m}$ rotates about its axis with an angular speed $100 \mathrm{rad} {\mathrm{s}}^{-1}$. The angular momentum of the cylinder about its axis is

An ice skater spins at $3\mathrm{ }\mathrm{\pi }\mathrm{ }\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{ }{\mathrm{s}}^{-1}$with her arms extended. If her moment of inertia with arms folded is$75\%$ of that with arms extended, her angular velocity when she folds her arms is

A bar of mass m length l is in pure translatory motion with its centre of mass velocity v. It collides with and sticks to another identical bar at rest as shown in figure. Assuming that after collision it becomes one composite bar of length 2l. The angular velocity of the composite bar will be.