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The easiest derivation of rod's moment of inertia?

  1. Jan 20, 2013 #1
    1. The problem statement, all variables and given/known data
    Derive the formula for rod's moment of inertia: I = ml2/12


    2. Relevant equations
    I = ml2/12


    3. The attempt at a solution
    The only one derivation I know of is dividing the rod into two parts and then integrating from 0 to l/2. However' I'd love to know if there's some easier (or more "natural"?) way to do it? Or, if not, maybe you know some website where it's explained as if I were five so that I can get the grasp of it? Because looking at bare integrals, I don't quite know what I'm calculating.
     
  2. jcsd
  3. Jan 20, 2013 #2

    rock.freak667

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    Homework Helper

    I think the easiest way would be to just do the integral.

    I= ∫ r2 dm

    If you consider a small infinitesimal piece at a distance 'dr' from the center of mass of the rod, the mass of this piece will be dm.

    Then you just use the fact that mass = mass per unit length * distance i.e. dm = M/L * dr
     
  4. Jan 20, 2013 #3
    I see. Thanks :)
     
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