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Moment of Inertia Teaser

  1. Oct 13, 2007 #1
    1. The problem statement, all variables and given/known data

    A cylinder with Radius R and mass M has a density that increases linearly with distance r from the cylinder axis, p =ar. (p is rho and a is alpha!) where a is a positive constant.
    a) Calculate the moment of inertia of the cylinder about a longitudinal axis through its center in terms of M and R.

    b)Is your answer greater and smaller than the moment of inertia of a cylinder of the same mass and radius but uniform density. Explain why this reason makes qualitative sense.

    2. Relevant equations

    I = int[r^2dm]

    3. The attempt at a solution

    I took a small "disc" of length a distance r from the longitudinal axis. The linear density at this point will be ar. The length of this disc will be dr so the mass of this small element will be ardr. Therefore, I = int[ar^3] from limits -L/2 to L/2. This comes out to be 0!!

    Please help me!! :cry:
  2. jcsd
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