When a ballerina pulls her arms in, her rotational kinetic energy increases because angular momentum is conserved. That means that work must have been done on her. I saw somewhere that there is work done because she has to pull her arms in against a centrifugal force.

I have two questions: what is this centrifugal force, and how is it that by pulling her arms in against this force, she has done work? A centrifugal force is a fictitious force from what I know of, so the kinetic energy increase cannot be accounted for with this. The second question is explained here:

Suppose you have some bar that you are holding at arm's length, perfectly horizontally (meaning ignore gravity). Because the bar is still, there is no net force. You now pull the bar towards you. The bar must have accelerated, so you did some positive work on the bar. However, because at the end of the process, when the bar is next to your body, it is at rest, you must have done negative work, decelerating the bar to make it come to rest. Therefore,the total work done on the bar must be zero. Note that this property does not depend on whether or not other forces are acting upon the bar, as it is only the net force that does work. So how is it, that by saying that there some force pulling the bar away from you (the centrifugal force for the ballerina), you have done work? It must be the same thing, because if the bar is at rest initially, and at rest when near your body, there must be no net force, so it is the same situation as if there was only one force applied to the bar.

We could say that you accelerated the bar and let the other force decelerate it, meaning that in all, you did work on the bar. However, the net work on the bar would be zero, because the other force did negative work on it by decelerating it. And we are interested in the net work done on the arms of the ballerina, not the work she does herself. So what part am I missing? Thanks for any answers and sorry for the long question.