Register to reply

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

by Jhenrique
Tags: curves, interia, moment, surfaces
Share this thread:
Jan25-14, 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?
Phys.Org News Partner Engineering news on
Hoverbike drone project for air transport takes off
Student develops filter for clean water around the world
Developing the next evolution in underwater communication
Jan25-14, 06:19 PM
Sci Advisor
HW Helper
PF Gold
P: 6,275
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 three-dimensional 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.
Jan25-14, 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.
Attached Thumbnails

Register to reply

Related Discussions
Moment of Inertia of Curves and Surfaces Classical Physics 1
Moment of interia Introductory Physics Homework 3
Moment of Interia Question Introductory Physics Homework 1
Moment of interia Introductory Physics Homework 2
Moment of Interia. Help please. Introductory Physics Homework 1