# First moment of area & second moment of area

This topic is still under development on wolframalpha and I've read some resources from wiki, youtube and yahoo answers and my basic understanding as of current is..

1st moment of area is area multiplied by the perpendicular distance from the point of line of action. 2nd moment of an area or moment of inertia is the moment of all small areas dA about any axis.

And I was wondering whether someone could give me some more information/examples on first and second moment of area (tech calculus, wouldnt let me add a new tag).

I'll bring the formula I'm trying to understand on this question tomorrow..

Thanks! :)

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Could you please add hyperlinks to those wiki resources which you read on this. Also, would it be correct that you define the $r$-th moment of region $D \subseteq \mathbb{R}^3$ as a rank $r$ tensor $\int_D \underbrace{(x \otimes \cdots \otimes x)}_{r \text{ times}} \mathrm{d} V$ ? – Sasha May 17 '12 at 5:01
@Sasha just came back to the question, thanks if you make an answer on the question, I'll select it as answered. – Killrawr Sep 11 '12 at 3:03

It makes sense to define $r$-th moment of a region $D \subseteq \mathbb{R}^n$ as $r$-th moment of the homogeneous solid body, occupying that region.
Thus, the $r$-th moment is defined as a rank $r$-tensor: $$I^{(r)}_{i_1,i_2,\ldots,i_r} = \frac{\int_D \left(x_{i_1} x_{i_2}\cdots x_{i_r}\right) \mathrm{d}V}{\int_D \mathrm{d}V}$$