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Finding Center of Mass - Plate with hole

  1. Oct 19, 2009 #1
    1. The problem statement, all variables and given/known data

    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 [Broken]

    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?

    2. Relevant 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.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Oct 19, 2009 #2


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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.
  4. Oct 19, 2009 #3
    This one is really getting me. The center of mass will be away from the hole. Now to translate into coordinates.
  5. Oct 19, 2009 #4


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    Imagine the force * distance downward for the mass of the entire plate, now imagine the hole is a mass * force upward
  6. Oct 19, 2009 #5
    So you essentially subract the larger mass from the other? I still dont see how to translate that into coordinates.
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