Moments of Inertia

Abstract

In considering the kinetics of a rigid body we shall meet the quantity Σ(δm)r² where δm is the mass of some particle at a perpendicular distance r from a particular axis. The summation symbol implies the addition of all the products indicated over the complete rigid body, and is termed the moment of inertia I with respect to the particular axis, which is then signified by a double subscript. For example I _xx is used to signify the moment of inertia about the x-axis through the origin (which is labelled X’X), Iz₁z₁ , signifies the moment of inertia about an axis Z₁’Z₁ which is parallel to, but displaced from, the z-axis (Z’Z) at the origin; for other special axes the moment of inertia may be signified by the axis itself and thus I_B’B is the moment of inertia about the axis B’B.