Past exam of the physics B course of the University of Cambridge / 2017 / Paper 1 / Section A / A2 / Solution

In steady rigid rotation of the liquid about its vertical axis, centrifugal acceleration is ${\Omega }^{2}r$ outward. Hydrostatic pressure balance in the rotating frame givesThe free surface is at constant atmospheric pressure, so its slope obeysCompare this parabolic free surface of a rigidly rotating liquid with $z-z_0=r^2/(4f)$. For focal length $f=1\mathrm{m}$,Either sense of rotation gives the same shape. The result assumes the liquid has reached rigid rotation before solidifying and that surface-tension and solidification distortions can be neglected.