Conservation of angular momentum experiment I've learned in that in this experiment:

...the skater will start rotating faster when she brings her arms in and there is no net torque acting on her. But what would happen to her angular momentum and rotation if she only brings one of her arms inwards with the other arm sticking outwards?
edit: will a net torque act on the body? What will this cause?
 A: The asymmetric problem gets into more complicated aspects of the kinematics of rotating bodies than are usually the point when presenting this example.
In the initial, arms out symmetric configuration, the skater's center of mass is directly over the pivot point.  If she brings one arm in, and still has the axis of her body strictly vertical, then her center of mass is no longer over the pivot point, and, were she not spinning, she would fall.  Now, because she is spinning, you are dealing with a problem similar to that of a gyroscope in a gravitational field whose axis of rotation is non-vertical: the gyroscope precesses.
More step wise
1. (initial condition) the skater is spinning about a vertical axis, both arms outstretched.
2. skater starts pulling her left arm inward, this changes the location of her center of mass.
3. skater starts "falling" towards her outstretched right arm.
4. this is a torque (due to gravity and the friction on the ground that keeps her skate tip at a fixed point on the ice) on a spinning body.
5. this ends up causing her main axis of rotation to precess.

I believe that I can see these kinds of effects in some of the examples here.  First thing to note is that the skate is always tracing a circle on the ice.  The size of this circle is related to the degree of asymmetry in the skaters body position: more asymmetric - larger circle.  This is consistent with the skater needing to manage the location of her center of mass by adjusting her body, in particular her legs, and/or  needing to manange rotating about a non-vertical axis in such a way that her overall angular momentum is (very close to) exactly vertical.
This page has a nice summary of rigid body mechanics, which if worked through, could be applied to this situation.
A: When she takes both her arms in, her moment of inertia decreases because the particles of her arms that were away from the axis of rotation have come closer to the axis. Now when she brings only one arm close to herself, obviously the same thing happens since again though half of the previous time but particles do come close to the axis of rotation.
Added after edit: why would internal forces cause torque, had there been a torque, net angular momentum would change but it does not, so no torque is applied.
