Moment of inertia with coordinates

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ehsan kuse
ehsan kuse on 11 Mar 2022
Commented: Sam Chak on 12 Mar 2022
Hello to all. Does anyone know how to get the moment of inertia by giving the coordinates of the points in matlab?
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Answers (2)

J Chen
J Chen on 11 Mar 2022
Moment of inertia is or , where m is the mass, r is the distance to the rotation axis.
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Sam Chak
Sam Chak on 12 Mar 2022
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.

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Image Analyst
Image Analyst on 11 Mar 2022
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.

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