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Moments of inertia using parallel axis theorem

  1. Sep 28, 2014 #1
    1. The problem statement, all variables and given/known data

    The mass of a homogenous thin plate is 36kg. Determine it moment of inertia about the x axis
    2vnqv5l.jpg

    2. Relevant equations

    Parallel axis theorem:
    Ix = Ix' + d^2*m

    3. The attempt at a solution

    p = m/a
    = 36/0.36 = 100

    Because the density is homogenous, I found the mass of the first rectangle:
    m = pa
    = 100*0.24
    = 24kg

    Ix = Ix' + d^2*m (MOI for the first rectangle)
    = 1/12*b*h^3 + d^2*m
    = 1/12(0.4)(0.6)^3 + (0.3)^2(24)
    = 2.1672

    Ix = Ix' + d^2*m (MOI for the second rectangle)
    = 1/12*b*h^3 + d^2*m
    = 1/12(0.4)(0.3)^3 + (0.15)^2(12).....................Mass of second rectangle = 36-24 = 12
    = 0.27

    Therefore MOI of the whole object = (MOI for the first rectangle) + (MOI for the second rectangle)
    = 2.44

    Problem is my textbook gives a total different answer which is 3.24. Please help, I am so confused
     
  2. jcsd
  3. Sep 28, 2014 #2

    Orodruin

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    This expression does not make sense since the two terms have different units (the first has unit length^4 and the second mass*length^2). I believe you are missing an insertion of the density in the first term.
     
  4. Sep 28, 2014 #3
    Oh yes, sorry. That should have been 1/12*m*h^2 + d^2*m. It now works out to 3.24. I mistakenly used the area moment of inertia formula instead of the mass moment of inertia formula. Thanks, :)
     
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