Moments of inertia of disks and spheres without integration

Calculation of moments of inertia is often challenging for introductory-level physics students due to the use of integration, especially in non-Cartesian coordinates. Methods that do not employ calculus have been described for finding the rotational inertia of thin rods and other simple bodies. ^1-3 In this paper we use the parallel axis theorem and the perpendicular axis theorem (both of which may be proved without calculus ⁴), along with rotational symmetry, to determine, without using integration, the moments of inertia of uniform disks and spheres.