angular momentum in a system? (coffee counter-rotating in a 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 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?
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 Recognitions: Science Advisor In translation, the sides of the cup provide a force on the oil layer that moves it with the cup. If the counter-rotation is not an optical illusion, it could be due to currents in the coffee below the oil layer. It could be that the bottom part of the coffee is rotating with the cup. This could lead to a vertical whirlpool that made the top part of the coffee counter-rotate.
 Mentor Blog Entries: 10 OxCOFFEE, welcome to PF. Yes, conservation of angular momentum is at play. You rotate the mug, but the liquid stays put because of the negligible torque applied to it by friction with the walls of the mug. I believe it only seems to rotate the opposite way, because relative to the mug it is rotating the opposite way. So that would be an optical illusion, just like treetops above you can appear to move opposite to clouds behind them that are drifting along. It may be as clem is suggesting, that some kind of convection or whirlpool gets set up to make things counter-rotate in reality. I'll have to check this out more next time I have some coffee.

angular momentum in a system? (coffee counter-rotating in a cup)

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 itself is not rotating with the same axis as the apparent counter-rotation of the liquid.

 Recognitions: Science Advisor I think the vertical whirlpool will work in the case you describe. However, if the liquid doesn't rotate, while you and the cup do, this could give the illusion of counter-rotation. Some illusions are more convincing than reality.

 Tags angular momentum, conservation, force, liquid, rotational inertia