If the ice at the poles of the Earth melts and flows towards the equator, will the angular velocity of the Earth increase or decrease?

If the radius of the Earth shrinks to half of its current value, the duration of the day will decrease by how many hours?

$A$ thin circular ring of mass $M$ and radius $R$ is rotating in a horizontal plane with angular velocity $\omega$ about an axis passing through its center and perpendicular to the plane. If another ring of the same size but mass $\frac{M}{4}$ is placed coaxially on the first ring,then the new angular velocity of the system is:

$A$ horizontal circular platform of radius $R = 0.5 \ m$ and mass $M = 0.45 \ kg$ is free to rotate about its axis. Two massless spring toy-guns,each carrying a steel ball of mass $m = 0.05 \ kg$,are attached to the platform at a distance $r = 0.25 \ m$ from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform,the balls have a horizontal speed of $v = 9 \ m/s$ with respect to the ground. The rotational speed of the platform in $rad/s$ after the balls leave the platform is:

$A$ particle is moving in a circular path. Which of the following statements is true?

$A$ circular stage is free to rotate about a vertical axis passing through its centre. $A$ tortoise is sitting at the corner of the stage. The stage is provided with an initial angular velocity $\omega_0$. If the tortoise starts moving along one chord at a constant speed with respect to the stage,then how does the angular velocity of the stage $\omega(t)$ vary with time $t$?