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Everyone knows how the surface of a spinning bucket of water would look like on earth - parabolic. But what if we turned off gravity (for instance by doing the experiment in a freely falling lift)? Would the surface be still parabolic? I'll explain my confusion in more detail.

The velocity of the spinning bucket is transferred to the water by means of frictional forces arising in the boundary between the bucket and water. But these frictional forces exist no matter whether there is gravity or not. So if I consider the whole bulk of water inside the bucket as a single system, this frictional force would give it a positive torque. Thus the water has to rotate. For the sustained rotation of water, a centripetal force has to exist. In normal gravity, the water surface changes its shape into a paraboloid so that there is a net force on any particle directed inward. But in free fall, there is no pressure on a particle inside the liquid. Thus the only force that can supply the centripetal acceleration is inter-molecular force between the particles which is weak to sustain huge velocities. So what exactly happens?

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I think you've already pretty much nailed the issue. You need to know the strengths/models of various inter-molecular forces (note that the frictional transfer is also via inter-molecular forces). For very thick fluid (think molasses instead of water), you maybe able to approximate the fluid as an elastic solid. But you'd probably expect an ideal fluid to exit the bucket in finite time. So I'd say it would depend on how you model water. – Willie Wong Jun 25 '11 at 16:45
up vote 6 down vote accepted

Assuming the bucket has a lid you will end up with most of the water lining the outside of the bucket.

This is how your basic artificial-gravity, spinning habitat works, after all.

Some water could, in principle, remain floating in the center but it is not stable.

If the bucket has no lid, the water oozes up against the sides and runs out the open end.

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Going by this space coffee cup video, surface tension would keep the water in the bucket:

Absent of pressure and temperature (pressure by molecules), the water would boil off and freeze.

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