thrown off

In article ,
Odysseus writes:
Is there a Hooke's-Law-like idealized
relation between angular speed and oblateness for an elastic ball?

The relation for liquids was worked out in the 18th(!) century. See
http://farside.ph.utexas.edu/teachin...ml/node38.html

Looking up "Maclaurin spheroids" and "Jacobi ellipsoids" will provide
more information. I think these are all based on constant density,
but there must be similar solutions for any specified density law.
The tricky bit is that for fast enough rotations, the body tends to
become non-axisymmetric. I never took the course that studied all
this stuff, though, so don't ask me for details.

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