Question about hot chocolate.?

If you take a cup of lets say hot chocolate, that has the white froth floating on the surface of the chocolate when its stationary and not moving around on the surface, and you hold that chocolate in your hand, keeping your hand and arm still, and then as you hold that cup in your hand you then make a half circle with your your arm, so the cup is like going around you or your body in a half circle, why the froth will turn clockwise if your moving your arm in the counter clockwise direction of the half circle, or vice versa? I understand that a swinging object, say on a string pulls straight outward, but why does the froth or liquid in the cup want to turn in the opposite direction , when its not air resistance moving it, as very little is even upon the top of the froth,,and all sides of the liquid is against the cup itself.