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1st and 2nd moment of interia of curves and surfaces 
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#1
Jan2514, 04:36 PM

P: 686

If I can to calculate the 1st and 2st moment of inertia of areas and volumes, I can compute for curves and surfaces too?



#2
Jan2514, 06:19 PM

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P: 6,474

First, you must define what you mean by the moment of inertia of a curve or surface.
The moment of inertia concept is useful in two areas: the second moment of area of a plane region or the mass moment of inertia of a threedimensional body. The first quantity is useful in analyzing the bending response of beams, while the second quantity is useful in calculating the motion of objects. 


#3
Jan2514, 07:50 PM

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: [tex]M=\begin{bmatrix} M_{yz}\\ M_{zx}\\ M_{xy}\\ \end{bmatrix} = \int \begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} dV[/tex] And the 2st like: [tex]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[/tex] Edit: the book this that the static moment (1st moment) is useful to calculate the geometric center. 


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