1st and 2nd moment of interia of curves and surfaces

by Jhenrique
Tags: curves, interia, moment, surfaces
 P: 686 In a book of mechanical projects (in portuguese, my natural idiom) I found an very surface explanation about first moment of curves and surfaces (see the anex), and I'm curious because I'd like to know if really exist a formula for 1st and 2nd moments of curves and surfaces. I understand the 1st moment as the follows formula: $$M=\begin{bmatrix} M_{yz}\\ M_{zx}\\ M_{xy}\\ \end{bmatrix} = \int \begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} dV$$ And the 2st like: $$I = \begin{bmatrix} I_{xx} & I_{xy} &I_{xz} \\ I_{yx} & I_{yy} &I_{yz} \\ I_{zx} & I_{zy} &I_{zz} \end{bmatrix} = \int \begin{bmatrix} y^2+z^2 & -xy & -xz\\ -yx & z^2+x^2 & -yz\\ -zz & -zy & x^2+y^2\\ \end{bmatrix} dV$$ Edit: the book this that the static moment (1st moment) is useful to calculate the geometric center. Attached Thumbnails