Stationary points of the rigid body kinetic energy and the principal axes of inertia

摘要

We demonstrate how searching for the extrema of the rotational kinetic energy can be exploited to introduce the idea of the principal axes of inertia in a general and intuitive way. To that end, we propose a motivational starting point for a discussion with students, followed by a physical problem that, in its simplest form, can be handled using only basic calculus. Principal axes and moments of inertia arise seamlessly as solutions to the proposed problem. A numerical example is provided to emphasize key ideas. To encourage alternative ways of thinking, we also show how similar conclusions can be derived from the square of the angular momentum. A generalized procedure, appropriate for a classical mechanics course, is outlined in the Appendix.