Isotropic inertia tensor without symmetry of mass distribution

Abstract

Conventional calculations of the inertia tensor in undergraduate physics course are usually done for highly symmetrical bodies. Students might therefore get the impression that the moment of inertia about any axis through the center of mass is the same only for bodies with the highest degree of symmetry relative to this point, e.g., for spheres. A simple, seemingly counterintuitive example is presented, showing that the moment of inertia of a non-regular body, here an assembly of material points, can be the same about any axis passing through its center of mass.