$A$ solid sphere is rotating in space. If the radius of the sphere is increased while keeping its mass constant,which of the following physical quantities will not change?

$A$ rotating table has an angular velocity $\omega$ and a moment of inertia $I_1$. $A$ man of mass $m$ stands at the center of the table. If the man walks a distance $r$ along the radius of the table,what will be his final angular velocity?

$A$ horizontal disc rotating freely about a vertical axis through its centre makes $90$ revolutions per minute. $A$ small piece of wax of mass $m$ falls vertically on the disc and sticks to it at a distance $r$ from the axis. If the number of revolutions per minute reduces to $60$,then the moment of inertia of the disc is .........

$M$ द्रव्यमान और $R$ त्रिज्या वाली एक डिस्क $x-y$ तल में चित्रानुसार गति कर रही है। दिखाए गए क्षण पर डिस्क का कोणीय संवेग क्या है?

State and explain the law of conservation of angular momentum.

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are $0.1 \; kg \cdot m^{2}$ and $10 \; rad \cdot s^{-1}$ respectively,while those for the second one are $0.2 \; kg \cdot m^{2}$ and $5 \; rad \cdot s^{-1}$ respectively. At some instant,they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is ........... $J$.