$A$ rotating table completes one revolution in $10 \ s$. Its moment of inertia is $100 \ kg \cdot m^2$. $A$ man of mass $50 \ kg$ stands at the center of the rotating table. If the man moves $2 \ m$ away from the center,what will be the angular velocity of the table in $rad/s$?

$A$ space station consists of two living modules attached to a central hub on opposite sides by long corridors of equal length $L$. Each living module contains $N$ astronauts of equal mass $m$. The mass of the space station structure is negligible compared to the mass of the astronauts,and the size of the central hub and living modules is negligible compared to the length of the corridors. Initially,the space station is rotating with angular velocity $\omega$ such that the astronauts feel an artificial gravitational field of strength $g = \omega^2 L$. Two astronauts,one from each module,move into the central hub. The remaining astronauts now feel an artificial gravitational field of strength $g'$. What is the ratio $g'/g$ in terms of $N$?

$A$ circular disc has a moment of inertia $I_2$ about an axis passing through its center and perpendicular to its plane. Another disc with a moment of inertia $I_1$ is placed on it. If the system rotates about the same axis with an initial angular velocity $\omega$,what will be the final angular velocity of the combined system?

$A$ swimmer can easily perform somersaults in the air while jumping from a height if he:

The angular momentum of a system of particles is not conserved:

$A$ person of $80\, kg$ mass is standing on the rim of a circular platform of mass $200\, kg$ rotating about its axis at $5$ revolutions per minute $(rpm)$. The person now starts moving towards the centre of the platform. What will be the rotational speed (in $rpm$) of the platform when the person reaches its centre?