bucket experiment

Newton imagined a water bucket {bucket experiment} [1689]. On Earth, bucket hangs on a rope and spins. At first, bucket rotates, but water does not, and water surface is flat. Then water rotates, and water surface becomes concave. If bucket slows and stops, water first rotates faster than bucket but then becomes less concave, and then becomes flat. What will happen if bucket rotates in outer space? What will happen if bucket rotates in empty space?

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