A gymnast standing on a rotating stool with his arms outstretched, suddenly lowers his arms :

his angular velocity decreases.

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his angular velocity increases.

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his moment of inertia decreases.

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his moment of inertia increases.

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Solution

The correct options are
A his moment of inertia decreases.
C his angular velocity increases.
By conservation of angular momentum $I_{1} ω_{1} = I_{2} ω_{2}$ ,
When gymnast will lowers his arms, the MI of of gymnast will decrease (because more mass is closer to axis of rotation) and angular velocity will increase.

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A gymnast standing on a rotating stool with his arms outstretched, suddenly lowers his arms :

The correct options are A his moment of inertia decreases. C his angular velocity increases.By conservation of angular momentum I1ω1=I2ω2,When gymnast will lowers his arms, the MI of of gymnast will decrease (because more mass is closer to axis of rotation) and angular velocity will increase.