The total angular momentum of all particles of a system is conserved if:

$A$ circular platform is free to rotate in a horizontal plane about a vertical axis passing through its center. $A$ tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity $\omega_0$. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform $\omega(t)$ will vary with time $t$ as:

$A$ particle is moving in a circular orbit of radius $r_1$ with an angular velocity $\omega_1$. It jumps to another circular orbit of radius $r_2$ and attains an angular velocity $\omega_2$. If $r_2 = 0.5\, r_1$ and assuming that no external torque is applied to the system,then the angular velocity $\omega_2$ is given by:

$A$ uniform disc of mass $m_0$ rotates freely about a fixed horizontal axis passing through its centre. $A$ thin cotton pad is fixed to its rim,which can absorb water. The mass of water dripping onto the pad per unit time is $\mu$. After what time will the angular velocity of the disc get reduced to half its initial value?

An object of mass $m$ is tied to a thin string,which is passed through a hollow tube. The tube is held in one hand and the string in the other. The object is rotated in a circle of radius $R$ with a velocity $v$. If the string is pulled downwards to decrease the radius,which of the following quantities remains conserved?

$A$ thin circular ring of mass $M$ and radius $r$ is rotating with a constant angular velocity $\omega$. Two particles,each of mass $m$,are attached to the opposite ends of a diameter of the ring. The new angular velocity of the ring will be: