product of inertia [′prä·dəkt əv i′nər·shə]
Product of inertia
(mechanics)
Relative to two rectangular axes, the sum of the products formed by multiplying the mass (or, sometimes, the area) of each element of a figure by the product of the coordinates corresponding to those axes.
Product of inertia
The product of inertia of area A relative to the indicated XY rectangular axes is IXY = ∫ xy dA (see illustration). The product of inertia of the mass contained in volume V relative to the XY axes is IXY = ∫ xyρ dV—similarly for IYZ and IZX.
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Product of inertia of an area
Relative to principal axes of inertia, the product of inertia of a figure is zero. If a figure is mirror symmetrical about a YZ plane, IZX = IXY = 0. See Moment of inertia
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