The water isn’t attached to the cup. The only force between the cup and the water is friction between the surface of the cup and the water molecules directly next to it. When you spin the cup, this force will push on the water a little bit, but not very much. If you keep spinning the cup, though, this friction will eventually cause the water to catch up with the cup and rotate along with it. But if you then stopped spinning the cup, the water would actually keep spinning and take a while to come to a stop, for the same reason.
If instead of liquid water, you had a block of ice frozen to the inside of the cup, then the molecules in the ice are all connected to each other and to the cup by rigid bonds. Thus, any force that you apply to the cup is also applied to the ice. So in that case you really can think of it as a single “unit”.
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