1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Moment of Inertia question

  1. Oct 5, 2008 #1
    1. The problem statement, all variables and given/known data
    Show that the rotational inertia of the rod about an axis through its center and perpendicular to its length is ML^2/12, where M is Mass and L is length from axis of rotation.

    2. Relevant equations

    3. The attempt at a solution

    Well, you see the integral that I did in the relevant equations? I got most of the work done there, assuming that R=L. My problem is understanding where the /12 comes from in the question. There were no numbers given in the initial question, just M and L.
  2. jcsd
  3. Oct 5, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Great. dm should have a dr in it. What's R? What are the limits on your integral? Take rho to be the density of the rod per unit length. What's M in terms of rho and L? What's the moment of inertia in terms of rho and L? Now eliminate rho.
  4. Oct 6, 2008 #3
    well, dm=pdL is what im assuming...

    so ∫dm=∫pdL

    but shouldnt the right side of the above equation be a definite integral while the left is an indefinite integral?

    i think the right side of the above equation should go from -L/2 to L/2, but that raises the question of the limits of the left side of the equation...

    either way, assuming both sides are indefinite integrals, substituting pL for M in ML^2 gives me


    but thats as much as i think i understood of your post.

    thanks for the quick reply.
  5. Oct 6, 2008 #4


    User Avatar
    Science Advisor
    Homework Helper

    Now you want to integrate r^2*rho*dr for r from -L/2 to +L/2 to get the moment of inertia. Then use M=rho*L to get rid of the rho.
  6. Oct 6, 2008 #5
    Okay, so....

    ∫(-L/2,L/2) pR^2dr= (1/3)R^3p|(-L/2,L/2)



    Thank you so much for your help.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook