Question

If a gymnast, sitting on a rotating stool with his arms outstretched, suddenly lowers his hands
A) The angular velocity decreases
B) His moment of inertia remains constant
C) The angular velocity increase
D) The moment of inertia increases

Answer 1

The law of conservation of angular momentum states that, angular momentum of a body doesn’t change, until any external torque acts on a body. Using this law of conservation of angular momentum we can solve this question.

Complete answer:
Angular momentum of a body is defined as the rotational equivalent of linear momentum. The rate of change of angular momentum of a body is equal to the torque applied on it. It implies that the angular momentum remains conserved when no external torque is applied. Here, since the friction between legs and stool is smaller; the net torque on the gymnast is zero. And since, the net torque is zero, angular momentum is conserved here.
We have angular momentum, $L=I\omega$
Where, $I$ is the moment of inertia and $\omega$ is the angular velocity.
Hence, when the hands are lowered, the radius of gyration reduces, which in turn reduces the moment of inertia of the body. And from the above equation, we can say that angular velocity is increased as the moment of inertia is decreased.

Therefore, the answer is option C.

Note:
Angular motion is similar to Newton's first law of motion, which states that, if no outside forces act on an object, an object at rest remains at rest and an object in motion remains in motion. Similarly, with rotating objects, we can say that unless an external torque is applied, a rotating object will keep rotating and an object at rest will not begin rotating.