Second Moments of Area

Polar Moment of Inertia

Area Moments of Inertia:figure Area moment of inertia is the name commonly used to describe the second moment of area. For example, consider an arbitrary area A shown at right. Its moment of inertia about the designated x-axis is given as

equation (1)

where y is the perpendicular distance measured from the x axis to the centroid of the differential area dA. Similarly the moment of inertia about the y-axis is given as

equation (2)

Application: The area moments of inertia are used extensively in mechanics of materials for calculations of flexural stress and deflection of beams as well as buckling stresses in columns.

Notice that if we consider the mass of the object instead of its area in Eqs. (1) and (2), then we obtain what are known as mass moments of inertia, which are commonly used in dynamic problems involving accelerating bodies.

Example 1 (LiveMath)

Example 2

Polar Moment of Inertia