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Moment of inertia of a cone

  1. Oct 22, 2008 #1
    1. The problem statement, all variables and given/known data

    Calculate the moment of inertia of a uniform solid cone about an axis through its center. The cone has mass M and altitude h. The radius of its circular base is R. (see attached photo)

    2. Relevant equations
    I know I need to somehow use the equation I= intergral r^2 dm
    also, I have an equation from my proffessor, dm=rho dv I'm not sure if I need this though since its unifrom density so it doesn't seem like [tex]\rho[/tex] should matter.

    3. The attempt at a solution
    I don't have a solution right now. I know the answer is 3/10 MR2 but I don't know how to get there. From class, since we did some examples, I think I need an equation that has a triple integral in it but I don't know what to integrate and to where. Do I need to get dm in terms of something like d[tex]\vartheta[/tex], dr, and dh?

    Thanks for your help. Also, if you have any general suggestions on how to complete moment of inertia problems like this that would be great. I know we're gonna be doing a lot of them.

    Thanks again!!!
    Last edited: Oct 22, 2008
  2. jcsd
  3. Oct 23, 2008 #2


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    Homework Helper

    Yes dm = [tex]\rho[/tex]dV will be used. Have you tried setting up dV in cylindrical coordinates? Then try to look for your limits of integration.
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