If no external torque acts on a system,which of the following remains constant in both magnitude and direction?

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

$A$ body changes its angular speed from $\omega_1$ to $\omega_2$ without any external torque applied. This change is due to a change in its moment of inertia. What is the ratio of the radii of gyration in the two cases?

$A$ person is sitting on a rotating stool with their arms outstretched. Suddenly, they fold their arms inward.

$A$ 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:

$A$ person is standing at the edge of a circular plate that is rotating with a constant angular speed about an axis passing through its center and perpendicular to its plane. If the person starts walking along the radius towards the axis, the angular velocity of the system will: