$A$ swimmer can easily perform somersaults in the air while jumping from a height if he:

$A$ thin circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane with an angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. If another disc of the same radius but one-fourth of its mass is placed gently on top of it,what will be the angular velocity of the new system?

$A$ 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:

$A$ thin and circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about its geometrical axis with an angular velocity $\omega$. If another disc of same dimensions but of mass $M/4$ is placed gently on the first disc coaxially,then the new angular velocity of the system is:

$A$ thin circular ring of mass $M$ and radius $r$ is rotating with a constant angular velocity $\omega$. Two particles,each of mass $m$,are attached to the opposite ends of a diameter of the ring. The new angular velocity of the ring will be:

Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to the disc and passing through the centre),and rotating with angular speed $\omega_1$ and $\omega_2$ are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the system in the process?