$A$ child is standing at the center of a rotating platform with hands folded. The kinetic energy of the system is $K$. The child now stretches his hands,doubling the moment of inertia. The kinetic energy of the system will now become ........

When a body is spinning on its axis in the absence of any external torque,choose the wrong statement.

$(a)$ $A$ child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of $40\; rev/min$. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to $2/5$ times the initial value? Assume that the turntable rotates without friction.
$(b)$ Show that the child's new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?

State and explain the law of conservation of angular momentum.

$A$ disc is rotating with an angular velocity $\omega$. $A$ child sits on it gently. Which of the following quantities will be conserved?

$A$ particle is moving in a uniform circular motion. At which point in the plane of the circle will the angular momentum of the particle be conserved?