Moment of inertia through scaling and the parallel axis theorem

Abstract

A right triangular plate scaled by a factor two generates a bigger plate composed of four triangular plates the same size as the original. By using dimensional analysis we write the moment of inertia around the center of mass, for the original and the bigger plate, in terms of a common unknown parameter. Through the parallel axis theorem we relate the moments of inertia of both plates and finally solve a very simple equation to find out the unknown parameter. This procedure avoids to calculate integrals. The result is extended to a scalene triangular plate by recognizing it is composed of two right triangular plates. We also review the parallel axis theorem in an appendix.

Moment of inertia: tricky ways

“…See e.g. [3][4][5]. In these articles using dimensional analysis and parallel-axis theorem the moment of inertia of a thin rod, and objects of the shape equilateral triangle, right triangular with equal cathetus, and rectangle were found.…”