$A$ 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?

$A$ disc with moment of inertia $I_1$ is rotating with an angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. Another disc with moment of inertia $I_2$ is placed on it,rotating about the same axis. What will be the combined angular velocity of both discs?

$A$ mass of $2 \ kg$ is moving in a circular path of radius $0.8 \ m$ with an angular velocity of $44 \ rad/s$. If the radius of the path becomes $1 \ m$,the new angular velocity will be ........ $rad/s$.

$A$ 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 standing on a turn-table is rotating at a certain angular frequency with his arms outstretched. He suddenly folds his arms. If his moment of inertia with folded arms is $75 \%$ of that with outstretched arms,then his rotational kinetic energy will

$A$ rotating table completes one revolution in $10 \ s$. Its moment of inertia is $100 \ kg \cdot m^2$. $A$ man of mass $50 \ kg$ stands at the center of the rotating table. If the man moves $2 \ m$ away from the center,what will be the angular velocity of the table in $rad/s$?