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

$A$ circular platform rotates in a horizontal plane about a vertical axis passing through its center. $A$ tortoise sits on the edge of the platform. The platform is given an initial angular velocity $\omega_0$. The tortoise now moves along a chord of the platform with a constant velocity (relative to the platform). How does the angular velocity $\omega(t)$ of the platform change with time $t$?

$A$ circular disc has a moment of inertia $I_2$ about an axis passing through its center and perpendicular to its plane. Another disc with a moment of inertia $I_1$ is placed on it. If the system rotates about the same axis with an initial angular velocity $\omega$,what will be the final angular velocity of the combined system?

$A$ swimmer,while jumping into a river from a height,easily forms a loop in the air if:

$A$ cockroach of mass $\frac{M}{2}$ starts moving with velocity $V$ on the circumference of a disc of mass $M$ and radius $R$. What will be the angular velocity of the disc?

$A$ uniform disc of mass $M$ and radius $R$ is rotating about a horizontal axis passing through its centre with angular velocity $\omega$. $A$ piece of mass $m$ breaks from the disc and flies off vertically upwards. The angular speed of the disc will be