Finding Center of Mass - Plate with hole

AI Thread Summary
To find the center of mass of a uniform circular plate with a hole, one must consider the plate's total area and the area of the hole. The center of mass formula involves the masses and positions of both the plate and the hole, treating the hole as a negative mass. The center of mass will shift away from the hole due to its removal. Translating this into coordinates requires careful calculation of the effective mass distribution. Understanding these principles is crucial for solving the problem accurately.
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Homework Statement



https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-09-Momentum/plate_with_hole/3.gif

A uniform circular plate of radius 11 cm has a circular hole of radius 3 cm cut out of it. The center of the plate is at the origin of the coordinate system and the center of the hole is located along the x-axis a distance 4 cm from the origin.

What is the position of the center of mass of the plate with the hole in it?

Homework Equations



center mass = (m1x1 + m2x2)/ (m1 + m2)

Im really stumped with this one. I was thinking at first to find the total area of the plate and then subtract that from the area of the hole. I am at a loss with this one.
 
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Almost right - imagine the hole as equivalent to a piece of metal that size/shape/position on the opposite side of the balnace.
 
This one is really getting me. The center of mass will be away from the hole. Now to translate into coordinates.
 
Imagine the force * distance downward for the mass of the entire plate, now imagine the hole is a mass * force upward
 
So you essentially subract the larger mass from the other? I still don't see how to translate that into coordinates.
 
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