Setup: A glass of red colored water is swung in a vertical circle.

Observations:  

• When the glass reaches the top of its arc the water remains in the glass.
• When the glass reaches the top of its arc the gravitational and the net force acting on the water are in the same direction. This is only true at the top of the glass's motion. In this positions we can treat the problem as though it was a circular motion problem with gravity acting down and a centrifugal force acting outwards on the water.
• Since the centrifugal force goes a mv²/r, the minimum velocity that the water can have at the top and still stay in the glass is when the weight of the water mg is equal to the centrifugal force. For a radius of one meter this would be 3.13 m/s or about 1/2 rev per second. A lot slower than the glass was actually moving.
• Observe that the minimum velocity does not depend upon the amount of water.