The falling cat problem has been very popular in control, mechanics and mathematics since Kane and Sher published a paper on this topic in 1969. A cat, after released upside down, executes a 180-degree reorientation, all the while having a zero angular momentum. It makes use of angular momentum conservation that is induced by rotational symmetry in the dynamics. In general, however, the angular momentum would not be conserved in the presence of a symmetry-breaking force. In this talk, I will discuss the effect of damping forces on the motion of mechanical systems with symmetry. As a corollary, I will provide a “dynamic” explanation of the famous experiment by G.I. Taylor on the “kinematic” reversibility of low-Reynolds-number flows.