If the earth were to suddenly contract to half of its present radius, what would be the duration of the day (in $text{ h}$)?

$A$ thin ring of mass $M$ and radius $R$ is rotating with an angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. If $4$ point masses each of mass $m$ are placed gently at the opposite ends of two mutually perpendicular diameters,what will be the new angular velocity of the system?

If the Earth were to suddenly contract to $\frac{1}{n}$ th of its present radius without any change in its mass, the duration of the new day will be nearly

$A$ boy runs and sits on a rotating platform. Which of the following quantities will be conserved?

$A$ 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?

$A$ mouse of mass $m$ jumps on the outside edge of a rotating ceiling fan of moment of inertia $I$ and radius $R$. The fractional loss of angular velocity of the fan as a result is