Polar moment of inertia

A schematic showing how the polar moment of inertia is calculated for an arbitrary shape about an axis o. ρ is the radial distance to the element dA.

Polar moment of inertia is a measure of a circular beam's ability to resist torsion. It is required to calculate the twist of an beam subjected to a torque. It is analogous to the area moment of inertia, which characterizes a beam's ability to resist bending and is required to calculate displacement.

The larger the polar moment of inertia, the less the beam will twist, when subjected to a given torque.

The polar moment of inertia must not be confused with the moment of inertia, which characterizes an object's angular acceleration due to a torque.

Unlike other forms of inertia, polar moment of inertia has units of length⁴ (SI m⁴)

See also moment (physics).

Other websites

• Torsion of Shafts - engineeringtoolbox.com
• Elastic Properties and Young Modulus for some Materials - engineeringtoolbox.com