# Moment of inertia with coordinates

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

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. 