$A$ 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?

$A$ ring of mass $M$ and radius $R$ is rotating about its axis with angular velocity $\omega$. Two identical bodies each of mass $m$ are now gently attached at the two ends of a diameter of the ring. Because of this,the kinetic energy loss will be

$A$ small object is attached to a light string which passes through a hollow tube. The tube is held by one hand and the string by the other. The object is set into rotation in a circle of radius $r_1$. The string is then pulled down,shortening the radius of the circle to $r_2$. The ratio of the new kinetic energy to the original kinetic energy is

The angular momentum of a particle performing circular motion under a central force is constant because of .........

$A$ thin circular ring of mass $M$ and radius $R$ is rotating with a constant angular velocity $2 \; rad \; s^{-1}$ in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring,the ring will then rotate with an angular velocity (in $rad \; s^{-1}$) of:

$A$ uniform heavy disc is rotating at a constant angular velocity $\omega$ about a vertical axis through its centre and perpendicular to the plane of the disc. Let $L$ be its angular momentum. $A$ lump of plasticine is dropped vertically on the disc and sticks to it. Which of the following quantities will remain constant?