Area Moment of Inertia
The area moment of inertia is the second moment of an area
around a given axis:
![$\displaystyle I_A = \int_A R^2(\underline{x}) dA
$](http://www.dsprelated.com/josimages_new/pasp/img2736.png)
![$ dA$](http://www.dsprelated.com/josimages_new/pasp/img2737.png)
![$ A$](http://www.dsprelated.com/josimages_new/pasp/img251.png)
![$ R(\underline{x})$](http://www.dsprelated.com/josimages_new/pasp/img2738.png)
Comparing with the definition of mass moment of inertia in §B.4.4 above, we see that mass is replaced by area in the area moment of inertia.
In a planar mass distribution with total mass uniformly
distributed over an area
(i.e., a constant mass density of
), the mass moment of inertia
is given by the area
moment of inertia
times mass-density
:
![$\displaystyle I_\rho \isdefs \int_M R^2 dM \eqsp \int_A R^2 \rho\, dA \eqsp \rho I_A
$](http://www.dsprelated.com/josimages_new/pasp/img2742.png)
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