Angular momentum of a particle rotating under a central force is constant due to

$A$ particle is moving in a uniform circular motion. At which point in the plane of the circle will the angular momentum of the particle be conserved?

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?

$A$ circular stage is free to rotate about a vertical axis passing through its centre. $A$ tortoise is sitting at the corner of the stage. The stage is provided with an initial angular velocity $\omega_0$. If the tortoise starts moving along one chord at a constant speed with respect to the stage,then how does the angular velocity of the stage $\omega(t)$ vary with time $t$?

Two discs of moment of inertia $I_1$ and $I_2$ and angular speeds $\omega_1$ and $\omega_2$ are rotating along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate together along the same axis,the rotational $KE$ of the system will be:

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