Moment of inertia with coordinates

Hello to all. Does anyone know how to get the moment of inertia by giving the coordinates of the points in matlab?

[James Tursa]

Please give us some context about your question. Currently your description is too vague for us to help. What is your overall problem you are trying to solve? What do you have to work with? How does the moment of inertia fit into this problem? Etc.

[ehsan kuse]

Well, I want to write a program in MATLAB that can calculate the geometric center of an object and the moment of inertia of a surface by taking the coordinates of the vertices of a shape. I'm currently having trouble writing code to calculate the moment of inertia around the x and y axes,

[James Tursa]

Is all the mass concentrated at the vertices? Or is the mass distributed uniformly along planar surfaces formed by the triangles of the vertices? Or ...?

[ehsan kuse]

It is also the shape of a polygon. I will send you a picture of the code below

[ehsan kuse]

Answer 1

[J Chen]

Moment of inertia is or , where m is the mass, r is the distance to the rotation axis.

[ehsan kuse]

thank you. But in MATLAB I want to get a level of inertia around the axes. I know the manual solution, but I need the code.

[J Chen]

Represent the axis and mass locations as vectors. Use trigometry to project the location vectors to the axis and find r.

[Image Analyst]

@ehsan kuse, did you totally overlook my Answer below? It does that.

[Sam Chak]

Hey @ehsan kuse

The Coordinate alone is not sufficient. You still need to know where the axis of rotation is, as mentioned by @J Chen. Are the centroid coordinate (center or mass) and the axis of rotation collinear?

Take the bob as an example, which is typically a solid spherical mass m on the end of a pendulum system. The moment of inertia about its center of mass is given by

.

However, if the bob is suspended from a pivot using a cord (massless) or a rod (rigid), and it rotates about the pivot point, then the moment of inertia of the entire system (called pendulum) is calculated differently, depending whether it is a simple pendulum, or a compound pendulum.

You can explore the spatial moments of inertia program shared by @Image Analyst.

Answer 2

[Image Analyst]

Attached is my demo of how to get image moments. These are spatial moments of inertia about the center of the blob I identified. You could adapt it to just not segment the image and take the origin/centroid as the middle pixel (columns/2, rows/2) if you want.