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Second moment of area ?

  1. May 30, 2009 #1
    second moment of area ???

    1. The problem statement, all variables and given/known data

    In finding the metacentric height of a floating body ( G-center of gravity ,M-metacentric point ,B-buoyancy point )
    so if the object is stable then M should be above G .
    GM=BM-BG

    i have learned that BM=I/V (where I second moment of are about the horizontal center line ,and V is submerged volume)
    so if the object is a cylinder i can find I using Pi*d^(4)/64 ....but can i use the same equation if the cylinder is not a uniform one .


    And is it the same thing meant by
    1)second moment of area
    2)Moment of inertia
    Or are they two different values ?
    Can they be connected using a another varaible ?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 30, 2009 #2

    Hao

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    Re: second moment of area ???

    The second moment of area is similar to the moment of inertia except for one extremely important point:

    The moment of inertia includes an integral over density, [tex]\rho[/tex].
    [tex]I_{inertia} = \int \rho r^2 dA[/tex].

    The second moment of area does not.
    [tex]I_{area} = \int r^2 dA[/tex].

    Hence, for a uniform object, [tex]I_{inertia} = \rho I_{area}[/tex].

    Therefore, the second moment of area is independent of the uniformity of the body.
     
  4. May 30, 2009 #3

    tiny-tim

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    Science Advisor
    Homework Helper

    moment of inertia ~ second moment of area

    Hi Hao! :smile:

    You're right, and you're wrong!! :biggrin:

    For all normal physicists, you're right …

    but some structural engineers use the name https://www.physicsforums.com/library.php?do=view_item&itemid=31" for the second moment of area, so they can be the same (and in this case I suspect they are)! :rolleyes:
     
    Last edited by a moderator: Apr 24, 2017
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