The total angular momentum of all particles of a system is conserved if:

$A$ 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?

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

$A$ circular disc has a moment of inertia $I_2$ about an axis passing through its center and perpendicular to its plane. Another disc with a moment of inertia $I_1$ is placed on it. If the system rotates about the same axis with an initial angular velocity $\omega$,what will be the final angular velocity of the combined system?

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

An equilateral triangle $ABC$ is made of a uniform wire. Two identical beads are initially at $A$. The triangle is set to rotate about a vertical axis $AO$. The beads are then released simultaneously from rest to slide down along $AB$ and $AC$. Neglecting friction,which quantities are conserved as the beads slide down?