Center of mass of metal square with a hole

AI Thread Summary
To find the center of mass of a metal square with a hole, first calculate the center of mass for the full square and the circle separately. Next, determine the masses of the full square, the circle, and the remaining shape after the hole is cut out, using area multiplied by density. The density will cancel out in the final calculations, simplifying the process. Combining the centers of mass requires a specific formula or integral approach. Understanding these steps is crucial for accurately determining the overall center of mass.
Elbobo
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Homework Statement


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Homework Equations





The Attempt at a Solution


I tried finding the center of mass of the square as if there were no hole in it, and then I added the radius of the circle to the x-coordinate of that. It's wrong, and I'm not sure how to approach it.
 
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Well, you can get started by writing down the coordinates for the center of mass of the full square (without the cutout) and the coordinates for the center of mass of the circle. Also calculate the masses of the full square, the circle and the square with the circle cut out. I guess you don't know the mass of each square cm (or whatever the units are) so you'll have to express your masses as an area x density. I'm sure the density will cancel out when you calculate the combined center of mass.

Do you know how to combine the centers of mass? Maybe you have a formula for it. Do you know the integral formula for finding the center of mass?
 

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