1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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:

    • asdf.JPG
      asdf.JPG
      File size:
      15.3 KB
      Views:
      126
  2. jcsd
  3. Dec 1, 2006 #2

    HallsofIvy

    User Avatar
    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook