<P> In structural engineering, the second moment of area of a beam is an important property used in the calculation of the beam's deflection and the calculation of stress caused by a moment applied to the beam . The planar second moment of area provides insight into a beam's resistance to bending due to an applied moment, force, or distributed load perpendicular to its neutral axis, as a function of its shape . The polar second moment of area provides insight into a beam's resistance to torsional deflection, due to an applied moment parallel to its cross-section, as a function of its shape . </P> <Dl> <Dd> Note: Different disciplines use the term moment of inertia (MOI) to refer to either the x, y, or both of the planar second moments of area, I = ∫∫ R x 2 d A (\ displaystyle I = \ textstyle \ iint _ (R) x ^ (2) \, \ mathrm (d) A), where x is the distance to some reference plane, or the polar second moment of area, I = ∫∫ R r 2 d A (\ displaystyle I = \ textstyle \ iint _ (R) r ^ (2) \, \ mathrm (d) A), 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 . In math and physics, moment of inertia is strictly the second moment of mass with respect to distance from an axis: I = ∫ Q r 2 d m (\ displaystyle I = \ textstyle \ int _ (Q) r ^ (2) \ mathrm (d) m), 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 Q. The MOI, in this sense, is the analog of mass for rotational problems . In engineering (especially mechanical and civil), moment of inertia commonly refers to the second moment of the area . </Dd> </Dl> <Dd> Note: Different disciplines use the term moment of inertia (MOI) to refer to either the x, y, or both of the planar second moments of area, I = ∫∫ R x 2 d A (\ displaystyle I = \ textstyle \ iint _ (R) x ^ (2) \, \ mathrm (d) A), where x is the distance to some reference plane, or the polar second moment of area, I = ∫∫ R r 2 d A (\ displaystyle I = \ textstyle \ iint _ (R) r ^ (2) \, \ mathrm (d) A), 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 . In math and physics, moment of inertia is strictly the second moment of mass with respect to distance from an axis: I = ∫ Q r 2 d m (\ displaystyle I = \ textstyle \ int _ (Q) r ^ (2) \ mathrm (d) m), 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 Q. The MOI, in this sense, is the analog of mass for rotational problems . In engineering (especially mechanical and civil), moment of inertia commonly refers to the second moment of the area . </Dd> <P> The second moment of area for an arbitrary shape R with respect to an arbitrary axis B B ′ (\ displaystyle BB') is defined as </P>

What is the difference between second moment of area and moment of inertia
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