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Homework Help: Find polar moment of region inside circle r = 3 and outside cardiod r = 2 + sin 0

  1. Apr 13, 2005 #1
    Here is the problem:

    Find the polar moment of the region that lies inside the circle [tex]r = 3[/tex] and outside the cardiod [tex]r = 2 + \sin\theta[/tex]. Assume [tex]\delta = r\theta[/tex]

    Here is what I have:

    [tex]I_{0} = I_{x} + I_{y}[/tex]

    [tex]I_{0} = \int_{0}^{2\pi}\int_{2 + \sin\theta}^{3}\;r^3\;\theta\;\sin^2\theta\;dr\;d\theta + \int_{0}^{2\pi}\int_{2 + \sin\theta}^{3}\;r^3\;\theta\;\cos^2\theta\;dr\;d\theta[/tex]

    [tex]I_{0} = \int_{0}^{2\pi}\int_{2 + \sin\theta}^{3}\;r^3\;\theta\;dr\;d\theta[/tex]

    Is this the correct setup? I don't have to manually evaluate this one, I just need to setup the integral limits and the integrand. Thank you in advance!
  2. jcsd
  3. Apr 13, 2005 #2


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    Science Advisor
    Homework Helper

    It looks okay to me...The cardioide & the circle have only one common point (y=3)

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