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Homework Help: Find the center of mass of a semi-circular plate

  1. Jul 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the center of mass of a semi-circular plate of radius r

    Find the volume when the plate (above) is rotated around a line along its straight side

    2. Relevant equations

    2(pi) integral of r dr

    3. The attempt at a solution

    I honestly don't know how to do centroids. :-( I'd like to know how to actually solve this problem.
  2. jcsd
  3. Jul 14, 2008 #2
    Re: Centroids

    The x coordinate of the center of mass should be zero (intuitively).
    For the y coordinate, assuming that the mass is uniformly distributed, use this equation (which can generalize for x):
    ycentroid = [tex]\frac{\int\int_R y dA}{A}[/tex]

    The volume is thus computed from the theorem of Pappus which states that
    volume = (area of R) * (distance traveled by the centroid)
    where the distance traveled by the centroid is 2*pi*ycentroid

    Hope that helps, let me know if you need further clarification.
    (Also, the volume when rotated about the straight side should come out to be that of a sphere, which is 4/3*pi*r^3, so you can use that to make sure you did it right.)
    Last edited: Jul 14, 2008
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