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Thin rod nonuniform linear mass density

  1. Feb 10, 2012 #1
    1. The problem statement, all variables and given/known data

    A thin rod of total length L has a nonuniform density given by λ(x)=ae^-bx where x is distance from one end of the rod. What is the moment of inertia of the rod for rotations around the end at x=0. Measuring from x=0 to x=L

    2. Relevant equations
    λ(x)=ae^-bx
    Inertia=I=∫dmr^2
    dm=λ(x)dx
    r=x
    I=mr^2


    3. The attempt at a solution
    my answer is -e^(bL)a[L^2/b + 2L/b^2 + 2/b^3] + 2a/b^3

    I do not think this is correct because my units are not in mass*length^2
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 10, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It looks correct. a and b mus have dimensions. a is linear density, [a]=[mass]/[length] and =1/[length].

    ehild
     
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