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Instead of a flat disc one would expect the centrifugal forces to push it in..

The body is not in a container but suspended in air spinning horizontally (i.e. left to right or vice-versa) - how to do this could be challenging - but that is not the issue.

Answer: It is not prolate: http://www.youtube.com/watch?v=BxyfiBGCwhQ.

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This question is too imprecise to be answered; how spinning? in what container? How is "oval shaped (vertically)"? –  mbq Mar 10 '11 at 15:24
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No ;-) How suspended? If in no-gravity situation, this is mostly a tradeoff between c-f making it a disc and surface tension making it a sphere, but the result is oblate not prolate. –  mbq Mar 10 '11 at 15:43
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I "read" that this is about a liquid at zero gravity, but of course the rotation of such a "drop" would not lead to a prolate ellipsoid, but more approach a disk (As I understand "prolate") –  Georg Mar 10 '11 at 15:59
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I would have thought so too but I heard otherwise. (one of us must be mixed up, I take prolate to mean like rugby ball, en.wikipedia.org/wiki/Prolate_spheroid, and oblate to be like a disc..) –  markmnl Mar 10 '11 at 16:02
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A good general rule: Before asking "why," ask "whether." I'm not convinced that the phenomenon for which you're seeking an explanation actually occurs. Can you give a more specific example, or some sort of evidence that this occurs? –  Ted Bunn Mar 10 '11 at 20:35

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It isn't prolate. It's oblate. Centrifugal forces push stuff out from the center. Nearby surface elements of the liquid are tugged along by surface tension, flattening out the original shape into a disk.

If something were to take on a prolate shape, there would need to be forces along the axis of rotation, which don't exist for most fluids I can think of, but if you provide a counterexample we could probably explain it. Beyond that, I think you're just confused.

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Did You read the comments to this question? "Everthing was said already, but not by everybody" –  Georg Mar 10 '11 at 19:18
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@Georg I don't know what you're so angry about. The original question was "Why does <thing that doesn't exist> exist?" and the only correct answer is, of course, "It doesn't." Even if this was discussed in the comments, stack exchange doesn't work off of comments, it works off of answers. –  kharybdis Mar 11 '11 at 17:00
    
If You read the whole thread (including times of answers and comments) You might learn why. –  Georg Mar 12 '11 at 17:55

I don't know about liquids 'suspended in air', but a self-gravitating rotating fluid may take many shapes, not only oblate ones.

Jacobi has shown that at high enough spin rates the familiar oblate shape becomes unstable and turns into a triaxial ellipsoid. At even higher spins another instability appears (this one was described by Poincaré) and the system becomes pear-shaped.

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