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Imagine a hollow shell (with massless walls) filled with an incompressible, nonviscous fluid. How can one find effective moments of inertia of such a shell?
Obviously, when the shell is spherical, the moment of inertia is zero. If the shell is a cube, it seems that the moment of inertia is no larger than the moment of inertia of the fluid outside of the largest inscribed sphere. However, this isn't likely to yield correct results in general: moment of inertia for a spherical shell with 3 perpendicular crossbars through the middle is almost surely lower than that of all the fluid present there.
