If the radius of the earth becomes $x$ times its present value, the new period of rotation in hours is (in $x^2$)

$A$ 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?

$A$ 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?

Two coaxial discs,having moments of inertia $I_1$ and $\frac{I_1}{2}$,are rotating with angular velocities $\omega_1$ and $\frac{\omega_1}{2}$ respectively,about their common axis. They are brought into contact with each other and thereafter they rotate with a common angular velocity. If $E_f$ and $E_i$ are the final and initial total energies,then $(E_f - E_i)$ is

$A$ man is standing on the edge of a circular platform. The platform is rotating with a constant angular velocity about an axis passing through its center and perpendicular to its plane. If the man walks along the radius towards the axis, the angular velocity will ........ .

State and explain the law of conservation of angular momentum.