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I just wrote a medical entrance test, in which this question appeared

a person sitting firmly over a rotating stool has his arms stretched, if he folds his arms, angular momentum about the axis of rotation

a) increases

b) decreases

c) remains unchanged

d) doubles

and to my surprise the answer is option c, which means the angular momentum will remain constant, should I consider it as a key mistake or had I misunderstood the question??

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    $\begingroup$ I think you should consider it as a key mistake. It is important to know that isolated systems (in your particular case we can ignore friction) conserve angular momentum. Also, please type up the question, instead of posting it as a picture. $\endgroup$
    – Danu
    Apr 29, 2015 at 10:04
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    $\begingroup$ Angular momentum is conserved unless an external torque is acting. This should be a fundamental part of any budding physicist's knowledge. Make it so! $\endgroup$ Apr 29, 2015 at 10:08

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You're mistaken. If I visualize , the speed of rotation increases as the person's hands fold inwards, this indicates that the angular velocity increases. The net angular momentum however, remains conserved. (If we consider the system to be isolated, that is. For every isolated system, the angular and linear momentum is always conserved.)

Also, for the given system:

$$L=I\omega$$, where $I$, $L$, $\omega$ are the moment of inertia, angular momentum, and angular velocity respectively. $I$ depends on the mass distribution and the square of the distance of it from any chosen point. If the hands are drawn inwards, $I$ decreases (because the mass of the arms is closer to the center of mass of the system) , and hence $\omega$ increases, but $L$ remains constant.

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    $\begingroup$ If this answer helped you you should check it , according to the rules here $\endgroup$
    – anna v
    Apr 29, 2015 at 10:32

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