Where Is the Center of Mass in a Plate with an Off-Center Hole?

AI Thread Summary
To find the center of mass of a uniform circular plate with an off-center hole, the problem involves using subtraction rather than integration. The center of the larger circle is at point C, while the center of the hole is at point C', located 0.80R from C. The approach suggests treating the cut-out hole as a negative mass disc superimposed on the original plate. This method simplifies the calculation by allowing the use of basic principles of mass distribution. The final position of the center of mass can be expressed in terms of R, as indicated in the hints provided.
sweatband
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Homework Statement



A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The center C' of the smaller circle is a distance 0.80R from the center C of the larger circle. What is the position of the center of mass of the plate?

Homework Equations



Hints:
subtraction is to be used
answer expressed in terms of R

The Attempt at a Solution



I believe integration is required to solve this, but I do not know where to begin.
 
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If anyone knows of a link they could send me that could lead me in the right direction, please let me know!
 
sweatband said:
I believe integration is required to solve this, but I do not know where to begin.

On the other hand, I believe, if you know that centre of mass of a circle is at its centre, you do NOT need to worry about integration: addition (or, 'subtraction' as the hint says) will suffice!

HINT: The portion that has been cut out, you can assume that a disc of negative mass was superimposed in that portion! (Of course, of same magnitude of uniform mass density as the first one.)
 

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