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 length^{4} (SI m^{4})

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