1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Deriving moment of Inertia

  1. Nov 12, 2009 #1
    I'm attempting to derive the moment of inertia for a cylindrical object.

    I know that I=[tex]\int r^2 dm[/tex]

    which equals =[tex]\int r^2 p dV[/tex]

    My question begins here, the derivations I seen pull p out of the integral, which makes sense to do, because in this case it's a constant. p=M/([tex]\pi[/tex]r^2L). So if I don't pull p out before integrating I get I=Mr^2, if I do pull it out, I get I=M/2r^2. I know the answer should be I=M/2r^2 because I have a solid cylindrical object. So why am I getting a different result when I leave p in, & a different result when I pull p out or am I just making a silly math error?

    Below is my work when I leave p inside the integral

    I=[tex]\int r^2*p*(2\pi*r)dr[/tex]
    =2M[tex]\int r dr[/tex] (replacing p with M/([tex]\pi[/tex]r^2L) before integrating)
    =Mr^2
     
  2. jcsd
  3. Nov 12, 2009 #2
    I believe that density is constant for each material.

    p/s: you replace m = DV, then you replace D = M/V... I dont get it :(
     
  4. Nov 12, 2009 #3
    I replaced dm with pdV & then p with M/V.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?