A dancer is spinning on a rotating table with his arms extended, if he folds his arms then the angular velocity will:

CONCEPT:

Angular Momentum:

• It is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object. It is a vector quantity

​
⇒ L = Iω

where I = moment of inertia and ω = angular velocity

EXPLANATION:

The angular momentum of a body is given as,

​⇒ L = Iω

If the angular momentum is constant, then,

\(\Rightarrow \omega \propto\frac{1}{I}\)     ---(1)

• Since there is no external torque is acting on the dancer, so his angular momentum will remain to conserve when he folds his arms.
• When the dancer folds his arms his moment of inertia decreases so the angular velocity increases. Hence, option 1 is correct.