Polar Moment of Inertia

The area polar moment of inertia is defined as Since x and y form the Cartesian coordinate system, the distance r can be expressed as Thus, the polar moment of inertia is simply the sum of Ix and Iy. The polar moment of inertia is often denoted by J, and is used in calculations of torsional stress and twist angle of bars.

The calculation of polar moment of inertia is demonstrated in the following example.