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My question is about Newton's bucket experiment. If a sphere filled (say) one-third with water is rotated very very fast, will the water eventually spread out across and coat the entire interior surface of the sphere? If so, then does this mean that the sphere's inside is coated with water whose inertial force is everywhere at right angles to the surface? And if this is so, then does this phenomenon offer a primitive physical model for the topological "gluing" together of two 3-dimensional spheres to yield a 4-dimensional sphere (a 3-sphere), especially when the gluing is imagined according to the method of progressive longitudinal "slices"? (Unless it is better to imagine the two 3-d spheres "put through" each other point for point, accordingly with the mechanical, force-oriented nature of Newton's experiment?) I'm trying to visualize William Blake's Mundane Shell, which Bronowski first half-recognized as a 3-sphere in 1942.

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    $\begingroup$ This question does not seem to be about history, you should ask on Physics SE. $\endgroup$ – Conifold Jul 1 at 8:26
  • $\begingroup$ i don't think you're correct about the water in the sphere, unless you are rotating about all three axes simultaneously. Spinning the way the bucket does will force the water into a torus (i suspect). Check out the system Hamiltonian. $\endgroup$ – Carl Witthoft Jul 1 at 13:11

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