$A$ disc is rotating with an angular speed of $\omega$. If a child sits on it,which of the following is conserved?

$A$ uniform disc of mass $m_0$ rotates freely about a fixed horizontal axis passing through its centre. $A$ thin cotton pad is fixed to its rim,which can absorb water. The mass of water dripping onto the pad per unit time is $\mu$. After what time will the angular velocity of the disc get reduced to half its initial value?

If the radius of the earth is reduced to three-fourth of its present value without any change in its mass,then the duration of the day on earth will be . . . . . . hours $30$ minutes.

Two discs with moments of inertia $I_1$ and $I_2$ and angular speeds $\omega_1$ and $\omega_2$ are rotating about collinear axes passing through their centers of mass and perpendicular to their planes. If they are joined together to rotate about the same axis,the rotational kinetic energy of the system will be:

$A$ disc with moment of inertia $I_1$ is rotating with an angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. Another disc with moment of inertia $I_2$ is placed on it,rotating about the same axis. What will be the combined angular velocity of both discs?

If the Earth shrinks to $1/8$ of its original volume, while maintaining the same mass, then the duration of the day will be (in $hrs$)