Polar moment of inertia, abbreviated as J, (English area unit \(in^4\), Metric area unit \(mm^4\)), also called the second polar moment of area, describe the resistance of an objects cross-section to torsional (twisting) deformations. It is an extension of the concept of moment of inertia, which measures an object's resistance to rotational motion about a given axis. While the ordinary moment of inertia deals with bending or flexural deformations, the polar moment of inertia specifically quantifies an object's resistance to twisting.
The polar moment of inertia is crucial in the design of shafts, beams, and other structural elements that are subjected to torsional loads. It helps engineers determine the amount of twist a component will experience under applied torque and is essential for ensuring the structural integrity and safety of rotating machinery and other torsionally loaded systems