To clarify, I am spinning about my torso (like an ice skater, only much more slowly and carefully :-) , with the cup in my hand as my arm is extended away from me. I am not rotating the coffee cup about its center. As such I don't see how the counter-rotation could be illusory, as the cup...
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...