According to the principle of conservation of angular momentum, angular momentum:

$A$ uniform disc of mass $M$ is rotating with a constant angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. Let its angular momentum be $L$. $A$ drop of molten plastic falls onto the disc and sticks to it. Which of the following remains constant?

$A$ particle is moving in a circular orbit of radius $r_1$ with an angular velocity $\omega_1$. It jumps to another circular orbit of radius $r_2$ and attains an angular velocity $\omega_2$. If $r_2 = 0.5\, r_1$ and assuming that no external torque is applied to the system,then the angular velocity $\omega_2$ is given by:

$A$ person standing on a rotating table holds weights in their outstretched hands and is rotating. They suddenly pull their hands in close to their body. Which statement is true?

$A$ 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:

$A$ child with mass $m$ is standing at the edge of a disc with moment of inertia $I$,radius $R$,and initial angular velocity $\omega$. See the figure given below. The child jumps off the edge of the disc with tangential velocity $v$ with respect to the ground. The new angular velocity of the disc is