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Homework Help: A tricky intigration for rotational inertia

  1. Jun 10, 2010 #1
    1. The problem statement, all variables and given/known data
    alright, so i'm trying to find the rotational inertia of a urethane longboard wheel, and i need to integrate a section of it that looks like a truncated annular cylinder that looks something like this if you cut it in half


    2. Relevant equations
    just to be sure that i don't plagiarize or anything, i was hoping for more of a hint instead of a straight up answer if possible... question mark

    3. The attempt at a solution
    i first derived the equation for the rotational inertia of an annular cylinder (I=(1/2)M(R1^2+R2^2), then i used M=(density)V to find the mass, but i can't find the density unless i dump the wheel into a wet measure filled with water, and i really don't wanna do that.

    any ideas?

    Attached Files:

  2. jcsd
  3. Jun 10, 2010 #2


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    Homework Helper

    Your drawings look like you have a cylinder and then you removed a cone from it, so you can get the inertia like that.
  4. Jun 10, 2010 #3
    actually i figured it out, it just turned out that i needed to dunk the wheel in water no matter what. eh, all in the name of physics i guess
  5. Jun 12, 2010 #4

    Ben Niehoff

    User Avatar
    Science Advisor
    Gold Member

    Why not just put it on a scale and weigh it to find the mass?
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