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Proof for moment of Inertia of thin disc

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Its actually not a homework , i am just curious about this

    I have disc with a hole in middle , R1 is inner radius , R2 is outer radius , Mass M is the disc's mass . Let density of disc uniform .

    I did it this way . -

    λ.dA=dm
    λ.pie.r.dr=dm as Area=pie.r^2

    Let substute in the equation I = ∫( R^2).dm

    therefore I = ∫( p.pie.r^3 ).dr
    remove constants outside the integral therefore I =λ.pie∫r^3.dr
    integrate (0 to R )to get I = λ.pie.r^4/4
    using Mass = λ*pie*r^2

    therefore i get I = (MR^2)/4 for thin Disc

    As i have a hole therefore its I = M(R2^2-R1^2)/4

    But sadly this is incorrent :/ . It seems that I = M(R2^2-R1^2)/2 is the correct solution

    Please Help !!!!!!!!!!!! :O why my way is wrong :(
     
  2. jcsd
  3. Nov 27, 2011 #2
    you wrote,

    λ.pie.r.dr=dm

    Shouldn't there be a 2 in there? dA = 2.pie.r.dr ?
     
  4. Nov 27, 2011 #3
    Oh my god "Slap myself in face" Lol such a silly error :S !!!! .
     
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