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

State the law of conservation of angular momentum and explain it with the example of a girl sitting on a swivel chair.

$A$ uniform circular disc of mass $50 \ kg$ and radius $0.4 \ m$ is rotating with an angular velocity of $10 \ rad \ s^{-1}$ about its own axis,which is vertical. Two uniform circular rings,each of mass $6.25 \ kg$ and radius $0.2 \ m$,are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in $rad \ s^{-1}$) of the system is:

$A$ ring of mass $M$ and radius $R$ is rotating about its axis with angular velocity $\omega$. Two identical bodies each of mass $m$ are now gently attached at the two ends of a diameter of the ring. Because of this,the kinetic energy loss will be

$A$ disc of mass $1 \, kg$ and radius $0.1 \, m$ is rotating with angular velocity $20 \, rad/s$. What is the angular velocity (in $rad/s$) if a mass of $0.5 \, kg$ is placed on the circumference of the disc?

If the torque applied on a particle is zero,then its angular momentum will be: