# Are there any exceptions for law of conservation of angular momentum?

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??

• 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.
– Danu
Apr 29, 2015 at 10:04
• 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! Apr 29, 2015 at 10:08

$$L=I\omega$$, 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.