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Polar moment of areatorsion, in objects (or segments of objects) with an invariant circular cross section and no significant warping or out-of-plane deformation.〔Ugural AC, Fenster SK. Advanced Strength and Applied Elasticity. 3rd Ed. Prentice-Hall Inc. Englewood Cliffs, NJ. 1995. ISBN 0-13-137589-X.〕 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, , where x is the distance to some reference plane, or the polar second moment of area, , 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: , 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.'' ==Limitations== The polar moment of area cannot be used to analyze shafts with non-circular cross-sections. In such cases, the torsion constant can be substituted instead. In objects with significant cross-sectional variation(along the axis of the applied torque), which cannot be analyzed in segments, a more complex approach may have to be used. See 3-D elasticity. However the polar moment of area can be used to calculate the moment of inertia of an object with arbitrary cross-section. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「polar moment of inertia」の詳細全文を読む スポンサード リンク
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