Center of mass of metal square with a hole

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SUMMARY

The discussion focuses on calculating the center of mass for a metal square with a circular hole. The correct approach involves determining the center of mass for both the full square and the circular cutout, then using their respective masses to find the combined center of mass. Participants emphasize the importance of expressing masses in terms of area multiplied by density, as the density will cancel out in the final calculation. Additionally, the integral formula for finding the center of mass is highlighted as a crucial tool in this process.

PREREQUISITES
  • Understanding of center of mass concepts
  • Familiarity with integral calculus
  • Knowledge of mass density and area calculations
  • Experience with geometric shapes and their properties
NEXT STEPS
  • Study the integral formula for calculating the center of mass
  • Learn about mass density and its application in area calculations
  • Explore methods for combining centers of mass for composite shapes
  • Review examples of center of mass calculations for various geometric configurations
USEFUL FOR

Students in physics or engineering, particularly those tackling problems related to mechanics and center of mass calculations involving composite shapes.

Elbobo
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Homework Statement


http://img35.imageshack.us/img35/6177/uthw404.jpg


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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