$A$ thin uniform circular disc of mass $M$ and radius $R$ is rotating with angular velocity $\omega$ in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of the same radius but of mass $\frac{M}{2}$ is placed gently on the first disc co-axially. The new angular velocity will be

Due to global warming, if the ice in the polar region melts and some of this water flows to the equatorial region, then

$A$ 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?

$A$ 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 $O$.

$A$ metre stick is pivoted about its centre. $A$ piece of wax of mass $20 \,g$ travelling horizontally and perpendicular to it at $5 \,m/s$ strikes and adheres to one end of the stick so that the stick starts to rotate in a horizontal circle. Given the moment of inertia of the stick and wax about the pivot is $0.02 \,kg \cdot m^2$,the initial angular velocity of the stick is ........... $rad/s$.

$A$ man stands on a rotating platform with his arms stretched horizontally,holding a $5\; kg$ weight in each hand. The angular speed of the platform is $30$ revolutions per minute. The man then brings his arms close to his body,with the distance of each weight from the axis changing from $90\; cm$ to $20\; cm$. The moment of inertia of the man together with the platform may be taken to be constant and equal to $7.6\; kg\; m^2$.
$(a)$ What is his new angular speed? (Neglect friction.)
$(b)$ Is kinetic energy conserved in the process? If not,from where does the change come about?