What is "polar moment of inertia"

n. (context engineering English) A measure of a body's resistance to twisting; a measure of torsional strength.

Polar moment of inertia is a quantity used to predict an object's ability to resist torsion, in objects (or segments of objects) with an invariant circular cross section and no significant warping or out-of-plane deformation. It is used to calculate the angular displacement of an object subjected to a torque. It is analogous to the area moment of inertia, which characterizes an object's ability to resist bending and is required to calculate displacement.

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

Polar moment of area should not be confused with moment of inertia, which characterizes an object's angular acceleration due to a torque. See moment (physics).

''Note: It has become common to use "Moment of Inertia" (MOI) to refer to either or both of the planar second moment of area, $I = \int_A x^2\, \mathrm dA$, where x is the distance to some reference plane, or the polar second moment of area, $I = \int_A r^2\, \mathrm dA$, where r is the distance to some reference axis. In each case the integral is over all the infinitesimal elements of area, dA, in some two-dimensional cross-section. "Moment of Inertia" is, strictly, the second moment of mass with respect to distance from an axis: $I = \int_m r^2 \mathrm dm$, where r is the distance to some potential rotation axis, and the integral is over all the infinitesimal elements of mass, dm, in a three-dimensional space occupied by an object. The MOI, in this sense, is the analog of mass for rotational problems.''