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Some powerful methods to calculate moments of inertia

We develope several powerful methods to calculate moments of inertia for certain kind of objects such as thin plates, solids of revolution, solids generated by contourplots, etc, by using the symmetry properties of the figures. The formulae shown in this paper besides saving time and effort considerably, could also provide a deep insight about the properties of this fundamental quantity. In particular, minimization of moments of inertia for certain objects is carried out by using methods of variational calculus. Furthermore, the methods developed in this paper can be extended easily to calculate other physical quantities such as centers of mass, products of inertia, electric dipolar momenta etc.