  This paper presents some formulae to calculate moments of inertia for solids
of revolution and for solids generated by contour plots. For this, the symmetry
properties and the generating functions of the figures are utilized. The
combined use of generating functions and symmetry properties greatly simplifies
many practical calculations. In addition, the explicit use of generating
functions gives the possibility of writing the moment of inertia as a
functional, which in turn allows to utilize the calculus of variations to
obtain a new insight about some properties of this fundamental quantity. In
particular, minimization of moments of inertia under certain restrictions is
possible by using variational methods.
