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

Initial angular velocity of a circular disc of mass $M$ is $\omega_{1}$. Then two small spheres of mass $m$ are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

$A$ uniform heavy disc is rotating at a constant angular velocity $\omega$ about a vertical axis through its centre and perpendicular to the plane of the disc. Let $L$ be its angular momentum. $A$ lump of plasticine is dropped vertically on the disc and sticks to it. Which of the following quantities will remain constant?

$A$ uniform disc of radius $R$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ is moving with velocity $v$ on the surface and hits the disc at the periphery and sticks to it. The angular velocity of the system after the collision is:

$A$ block of ice is placed at the center of a circular table. The table rotates with an angular velocity $\omega$ about a vertical axis passing through its center. If the ice melts without evaporation,what will happen to the rotational speed of the system?

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity: