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Need help with this moment about the y

  1. Nov 30, 2006 #1
    1. The problem statement, all variables and given/known data

    Determine by direct integration the moment of inertia about the y-axis in the figure shown.

    2. Relevant equations
    See Iy on attached.
    Equation for curve also on attached.


    3. The attempt at a solution
    My answer didn't include pi, and the answer apparently does. I'm trying to do this via a double integral as opposed to using one integral and doing something funky. My problem I THINK is in finding dA.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Dec 1, 2006 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You are right. There is no "[itex]\pi[/itex]" in the solution.

    The moment of inertia of that figure, about the y-axis is
    [tex]\int_{x=0}^a\int_{y= -b\sqrt{1-\frac{x^2}{a^2}}}^{b\sqrt{1-\frac{x^2}{a^2}}} y dydx[/tex]
    That's easy to integrate and has no "[itex]\pi[/itex]".
     
  4. Dec 1, 2006 #3
    Hmm - that's what I thought. In fact, I think that's the exact integral that I had. I'll give it another go. Thanks!
     
  5. Dec 1, 2006 #4
    I lied - that's a y^2, not just a y in the integral. The answer is pi*a*(b^3)/8...Still no luck though.
     
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