What nonlinear deformations will a fast rotating planet exhibit?
This is really a basic physics question that I wanted to check myself on because I'm not entirely sure of the correct answer. I asked a puzzler question on the last episode of my podcast about hollow Earth claims. I asked people to imagine a sphere with a solid shell that was filled with a compressible material, and this was spun very rapidly. (1) Would a hollow form, and (2) what shape would that hollow take on if it did form?
My thinking is that, yes, a hollow would form, but it would not be spherical as the hollow Earthers claim. It would be a biaxial ellipsoid with the short axis oriented along the poles and the long axes to the equator. This is because the centrifugal forces at the equator due to the spin would be much greater than at the poles, so there would be no "outward force" at the poles.
Is this correct? If so, is that a good explanation for a lay audience? If not correct, then what is the solution (it's been a long time since I took classical mechanics)? Thanks!