If the mass of the Earth is kept constant and its radius is reduced to half, then the duration of the day will become ........ $hr$.

An ant is sitting at the edge of a rotating disc. If the ant reaches the other end, after moving along the diameter, the angular velocity of the disc will

$A$ 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:

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?

$A$ 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:

An equilateral triangle $ABC$ is made of a uniform wire. Two identical beads are initially at $A$. The triangle is set to rotate about a vertical axis $AO$. The beads are then released simultaneously from rest to slide down along $AB$ and $AC$. Neglecting friction,which quantities are conserved as the beads slide down?