Moment of inertia bar variable density

  1. Mar 19, 2011 #1
    1. The problem statement, all variables and given/known data
    I think I solved this correctly, but im not sure.

    Find the moment of inertia of a bar with density d=kx^2, where x is the distance from the center of the bar(find the moment of inertia at the center)

    THe length of the bar is L

    2. Relevant equations


    Moment of inertia=sum of mx^2

    3. The attempt at a solution

    FInd K. Well, the integral of density over a bar is the mass, so from the center, integrate kx^2 to half of the distance L, gives kx^3/(8*3)= M/2 k= 12M/(L^3)

    To find the moment of inertia, sum m1x1^2+m2x2^2...mnxn^2= integral x^2dm

    density =kx^2, so dm=kx^2dx

    Integrate 2k *x^4(over L/2)which equals 2k* L^5/(32*5)

    sub in k

    Moment of inertia of the bar equals 3/20 L^2

    Is this right? It seems low
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Moment of inertia bar variable density
  1. Moment of Inertia (Replies: 0)

  2. Moments of Inertia (Replies: 0)