Before diving into a swimming pool, a swimmer curls their body, because this

$A$ disc of mass $M$ and radius $R$ is moving with an angular velocity $\omega$ as shown in the figure. Find the angular momentum of the disc about the reference point $O$.

$A$ particle is moving in a circular path. Which of the following statements is true?

Consider a disc of mass $5 \,kg$ and radius $2 \,m$, rotating with an angular velocity of $10 \,rad/s$ about an axis perpendicular to the plane of rotation and passing through its center. An identical disc is placed gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is . . . . . . $J$.

$A$ ring of mass $M$ and radius $R$ is rotating with angular speed $\omega$ about a fixed vertical axis passing through its centre $O$ with two point masses each of mass $\frac{M}{8}$ at rest at $O$. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant,the angular speed of the system is $\frac{8}{9} \omega$ and one of the masses is at a distance of $\frac{3}{5} R$ from $O$. At this instant,the distance of the other mass from $O$ is

$A$ wheel is rotating freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is $I$ and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia $3I$ initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is: