I haven't thought about physics in long enough that this is stumping me. I have a coffee cup with (good) coffee in it. Since it is good coffee it has oils on the top. When I translate it linearly from side to side or from front to back (or any other linear direction) the oil stays stationary relative to the cup. When i move it in an arc horizontally (as when I rotate around my vertical axis with the cup in hand), the oil (and presumably the coffee in the cup) counter-rotates. That is to say, it appears that the oil rotates clockwise when I rotate counter-clockwise, and vice versa. My gut reaction is "conservation of angular momentum explains this", but I'm not able to put my finger on just why this is so. Am I on the right track?