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Chapter 10 Moments of Inertia

Area moments of inertia are a measure of the distribution of a two-dimensional area around a particular axis. Fundamentally, the portions of a shape which are located farther from the axis are more important than the parts which are closer. The primary application is in structural engineering and machine design where they are used to determine a structural member’s stiffness. Another application is in Fluid Mechanics where they are used to determine the effect of pressure on a submerged surface. We will use the symbol \(I\) for this property, along with a subscript to indicate the specific axis, so for example, \(I_x\) would indicate the “Area moment of inertia with respect to the \(x\) axis.”

The mass moment of inertia you learned about in Physics is not the same as the \(area\) moment of inertia in Statics!

This can be confusing since both are commonly shortened to “moment of inertia” and both use the same symbol, \(I\text{.}\) They have different units however, and the intended moment of inertia can easily be determined from context or with a unit analysis.