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!

Moment of Inertia tensor SETUP, not to difficult but cant figure it out

  1. Feb 16, 2008 #1
    [SOLVED] Moment of Inertia tensor SETUP, not to difficult but cant figure it out

    1. The problem statement, all variables and given/known data
    a) For a cylinder of mass M, radius R and height h, calculate the inertia tensor about the center of mass. What are the principal axes?

    2. Relevant equations

    [​IMG]

    3. The attempt at a solution
    I need help with setting up the integral. I placed the origin at the center of the cylinder. So and i set my boundaries as = z going from -h/2 to h/2, y going from -R to R and x going from -sqrt(R^2-y^2) to sqrt(R^2-y^2).

    However when i integrate Ixx I get zero and I know I am not suppose to. Is there a better choice for my boundaries?? My x boundaries are the problem here because they give me a ugly answer.

    Thanks
     
  2. jcsd
  3. Feb 16, 2008 #2
    Try to use cylindrical coordinates, this will simplify the problem.
     
  4. Feb 16, 2008 #3
    so for Ixx will the integral be
    r^2sin^2(theta) + h^2 r^2sin(theta)dr d(theta) dz??

    thank you
     
    Last edited: Feb 16, 2008
  5. Feb 16, 2008 #4
    Not shperical coordinates, cylindrical ones! :smile:

    [tex]x=r\,\cos\phi,\,y=r\,\sin\phi \Rightarrow d\,x\,d\,y\,d\,z=r\,d\,r\,d\,\phi\,d\,z[/tex]

    thus [itex]I_{xx}[/itex] reads

    [tex]I_{xx}=\int_V \rho(r,\phi,z)\,\left(r^2\,\sin^2\phi+z^2\right)\,r\,d\,r\,d\,\phi\,d\,z[/tex]
     
    Last edited: Feb 16, 2008
  6. Feb 16, 2008 #5
    got it!! I feel so dumb spending so much time trying to figure it out in cartesian coord. Thank you so much!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Moment of Inertia tensor SETUP, not to difficult but cant figure it out
Loading...