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Moment of area need quick!

  1. Sep 18, 2009 #1
    1. The problem statement, all variables and given/known data

    the moment of area is integral (r^2 dA). With r measured from the origin, use geometry to evaluate this integral in both orders.

    2. Relevant equations



    3. The attempt at a solution
    Ok so I set up the integral with dA=rdrd(theta) so with r from 0 to r and theta from 0 to pi/2. i ended up with pir^4/8 which i multiplied by for to account for each quadrant and ended up with (pir^4)/2.
    is this correct? incorrect? why? i don't really get what the moment refers to. and also, if i am evaluating the correct integral. please help!
     
  2. jcsd
  3. Sep 18, 2009 #2

    tiny-tim

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    Hi briteliner! :smile:

    (have a pi: π and an integral: ∫ and try using the X2 tag just above the Reply box :wink:)
    (this is the second moment of area … it measures a body's resistance to bending stress perpendicular to a particular axis :wink:)

    What shape are you trying to find the moment of area of, and about what axis? :confused:
     
  4. Sep 18, 2009 #3
    a triangle, with x and y axis i think
     
  5. Sep 18, 2009 #4

    tiny-tim

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    grrr! what shape of triangle? :rolleyes:

    Anyway, you don't need r and θ for a triangle

    just use dxdy as usual …

    show us what you get. :smile:
     
  6. Sep 18, 2009 #5
    if b is the height and a is the width, i get (3(b^3)(x^3))/(y^3)
     
  7. Sep 18, 2009 #6

    tiny-tim

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    (try using the X2 tag just above the Reply box :wink:)

    How can x and y be in the answer?

    It should just have a and b.

    (btw, is this a right-angled triangle? and you still haven't said what the axis is)

    Anyway, show us your full calculations next time. :smile:
     
  8. Sep 18, 2009 #7
    You're in Nearing's class, aren't you? lol

    Pic is a right triangle with vertices at (0,0), (a,0), and (a,b).

    Recall how to change the integrand so that you can integrate properly. (How is r related to x and y if you choose to integrate with respect to x & y?)
     
    Last edited: Sep 18, 2009
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