Moments and Product of Inertia
Moments and Product of Inertia:
Consider a three dimensional body of mass m as shown. The mass moment of inertia I about the axis O-O is defined as,
where r is the perpendicular distance of the mass element dm from the axis O-O and where the integration is over the entire body. For a given body, the mass moment of inertia is a measure of the distribution of its mass relative to the axis in in question and for that axis is a constant property of the body. In SI units, the units of measurement of inertia are kg-m2 .
Consider the body of density shown below :
dV is the volume of a infinitesimal volume element.
The term Ixx, Iyy and Izz are called the mass moment of inertia of the body about the x, y and z axes respectively. Note that in each such case, we are integrating the mass element , times the perpendicular distance squared from the mass elements to the coordinate axis about which we are computing the moment of inertia.