Squashing Method for Moment of Inertia Calculations

Abstract

Moments of inertia (MOIs) are usually derived via substantial integration and may intimidate undergraduates without prior backgrounds in calculus. This paper presents an intuitive geometric operation, termed “squashing,” that transforms an object into an equivalent one with a reduced dimension, whose MOI is simpler to determine. The combination of squashing and other methods (e.g., scaling arguments, the perpendicular-axis and parallel-axis theorems) enables the computation of complex MOIs with minimal integration.

Vibration Measurement of a Screening Machine

“…The tensor of moment of inertia referring to the centre of gravity, is denoted by . The entries of the moments of inertia tensor are determined by the following assumptions [7]:…”