$A$ person is standing at the edge of a circular plate that is rotating with a constant angular speed about an axis passing through its center and perpendicular to its plane. If the person starts walking along the radius towards the axis, the angular velocity of the system will:

$A$ mass is whirled in a circular path with constant angular velocity and its linear velocity is $v$. If the string is now halved keeping the angular momentum same,the linear velocity is

$A$ cube of side '$a$' moves with a velocity '$v$' on a horizontal surface as shown in the figure. It hits an edge at point '$O$'. What will be the angular speed of the block after it hits point '$O$'?

$A$ uniform disc of mass $M$ is rotating with a constant angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. Let its angular momentum be $L$. $A$ drop of molten plastic falls onto the disc and sticks to it. Which of the following remains constant?

$A$ stone of mass $m$,tied to the end of a string,is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually,keeping the angular momentum of the stone about the centre of the circle constant. Then,the tension in the string is given by $T = Ar^n$,where $A$ is a constant and $r$ is the instantaneous radius of the circle. The value of $n$ is equal to

$A$ torque is applied to a body,changing its angular velocity from $\omega_1$ to $\omega_2$. What is the ratio of the initial radius of gyration to the final radius of gyration?