I have been thinking on the following problem.
Part I. Imagine we have a mouse enclosed in a rigid box. We placed the box on a frictionless surface (ice might be a good example). Can the box start moving because of something the mouse is doing inside? My answer to this question is: The center of mass of the combined system (mouse + box) will NOT move because there are no external forces and the internal forces satisfy at least the weak form of Newtons Third Law. So, Momentum is conserved for the system.
Part II. Now we put the mouse in a rigid wheel and we put the wheel on a frictionless surface or we suspend the wheel from its center on frictionless bearings. Can the wheel start rotating because of something the mouse is doing inside? My intuition will say YES it will move because I have seen this system in several pet stores and mice can actually rotate wheels. But I was trained in classical mechanics so, I know that the system must conserve angular momentum if there are no external torques and the internal forces satisfy the strong version of Newton's third law. So, How does it work in this case, I came with different ideas on how to reconcile the experiment with the theory but I don't like them very much. I want to get new insights.