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Calculus III: Center of Mass

  1. Oct 22, 2007 #1
    Question Details:
    I have two circles centered at the origin, one with radius A and the other with radius b.

    Looking at the hemiwasher (area between) the circles form above the x axis, find the values of A and B that place the center of mass within the hemiwasher itself, not in the open middle space.

    What i think i has solved so far: not necesseraly accurate:
    I solved the Y value of the center of mass in terms of A and B to be:

    :Y= (4(A^2+AB+B^2))/(3pi(A+B))

    Please Help!

    how can I use this to find values of a and b that put the y coordinate of the center of mass between a and b?

    B is the smaller radii; the density is constant, so it is irrelvant.
    Last edited: Oct 22, 2007
  2. jcsd
  3. Oct 22, 2007 #2


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    Staff Emeritus
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    In other words, you want Y between A and B. You need to find A and B such that
    [tex]A\le \frac{4(A^2+AB+ B^2)}{3\pi (A+B)}\le B[/tex]

    You won't be able to find specific values of A and B, of course. You want to find a relation between A and B that will guarentee that inequality. I would recommend that you look at
    [tex]A\le \frac{4(A^2+AB+ B^2)}{3\pi (A+B)}[/tex]
    [tex]B\ge \frac{4(A^2+AB+ B^2)}{3\pi (A+B)}[/tex]

    Those should give you two relations between A and B. Both need to be satisfied.
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