Test analysis: (1) The critical condition for the cup and water to pass through the highest point is that gravity just completely plays the role of centripetal force, so solve it.
(2) At the lowest point, the tension of the rope is the largest, so there is a solution, so the speed cannot be exceeded.
Comments: Take the water and the cup as a whole and do circular motion. When passing through the highest point, the speed of the rope is minimum when the Zhang Liwei is 0; Lowest point, maximum rope tension, maximum speed.