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: Derivation of moment inertia formula

  1. Apr 10, 2008 #1
    How do I derive the formula 1/12 Ml^2?
    Derive the formula for moment of inertia of a uniform thin rod of length l about an axis through its center perpendicular to the rod.
  2. jcsd
  3. Apr 10, 2008 #2
    There are a few ways to do it. Moment of inertia is calculated by
    [tex]\int R^2.dm[/tex]

    So place x=0 at the centre, the x-axis running along the rod. So you're integrating from -l/2 to l/2.
    We must find dm in terms of our integration variable x. In dx we have an element of mass dm.
    mass = (density)(volume)=(density)(cross-sectional area)(length)

    dm = p.A.dx
    where p is the density and A the cross-sectional area. Our integral is now:
    [tex]\int_{-l/2}^{l/2} pAx^2.dx[/tex]
    If you work it out you find it equals:
    [tex]\frac{1}{12} pAl^3[/tex]

    but if we remember that mass = pAl, then we get 1/12 Ml^2.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook