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Radius of gyration (rectangle)

  1. Nov 24, 2009 #1
    I'm trying to figure out the radius of gyration of the frame about O.

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

    A rectangular frame is put together with massless rods having identical 1.8 lb weights placed at the corners as shown in the figure. The frame is pivoted about an axis passing through O, the center of mass of the system, perpendicular to the paper.
    a) Find the angular acceleration of the frame about O
    b) Find the radius of gyration of the frame about O


    2. Relevant equations
    Angular acceleration of the fram about O =
    Icm = 1/12(M(a2 + b2))
    Icm = 101.4kg ft2

    I can't find an equation for b) and I can't find anything about "radius of gyration" in my book. Is there another name for it?

    I found R = [tex]\sqrt{I/m}[/tex] On wiki & a few other sites..

    3. The attempt at a solution

    [tex]\sqrt{101.4kg ft^2 / 7.2kg}[/tex]

    =

    3.75ft
     
    Last edited: Nov 24, 2009
  2. jcsd
  3. Nov 24, 2009 #2

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    You have the correct expression for the radius of gyration. I know of no other name for it.

    Your calculation of the moment of inertia looks suspicious, but to be 100% sure, we have to see a picture. I say "suspicious" because the rods are said to be massless so the factor of 1/12 should not be there. Just find the total moment of inertia of the four masses at the corners because that's what the problem appears to want.
     
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