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How to determine rectangular and polar radii of gyration?

  1. Apr 25, 2015 #1
    1. The problem statement, all variables and given/known data

    Determine the rectangular and polar radii of gyration of the shaded area about the axes shown.

    Snapshot_zpsemlzcj6q.jpg

    2. Relevant equations
    dIx = y2dA
    Ix = ∫y2dA

    dA = ydx
    A = ∫(dA

    3. The attempt at a solution
    dIx = y2dA
    =(x6/16) *(x3/4) dx
    =(x9/64)dx
    Ix =(integrating from 1 to 2) ∫dIx = 1023/640

    dA = ydx
    A = (integrating from1 to 2)∫(x3/4)dx = 15/16

    kx = √(Ix/A) = 1.705

    I am getting the radius of gyration about y axis correctly but that baout x axis is wrong.
    The actualy answer given is 0.75. I am unable to figure out where I am going wrong.
     
  2. jcsd
  3. Apr 25, 2015 #2

    BvU

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    No, my mistake, let me re-think, or rather: think about this one some more.
    One at the time: start with Ix:
    Yes: work it out dA bit more and you'll see you miss a factor 1/3 in Ix.

    By the way, you confuse me with ##k_x =\sqrt{I_x/A} = 1.705##; I get ##1.306\;##; a typo ?​
     
    Last edited: Apr 25, 2015
  4. Apr 26, 2015 #3
    Yes. Sorry I forgot to take the square root so yea a typo.
    But to be honest, I don't get what you are saying. Could you be more specific in where I am going wrong?
     
  5. Apr 26, 2015 #4

    BvU

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    ##dI_x = y^2 dA## needs to be worked out to ##dI_x = y^2 dy dx##: it's a double integral. You seem to treat it as a single one.
     
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