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Moment of inertia of disk about off centre axis

  1. Apr 22, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the moment of inertia of a uniform disk of mass m and radius r about an axis normal to the disk, through a point x from the centre.

    2. Relevant equations



    3. The attempt at a solution

    Let ρ be the density. I=ρ∫r^2 dA=ρ∫∫r^3 dr dθ in polar coordinates.
    However I don't know what the limits of r should be. θ is between 0 and 2 pi, but r max varies, so I'm confused.
     
  2. jcsd
  3. Apr 22, 2012 #2
    use parallel axis theorem
     
  4. Apr 22, 2012 #3

    ehild

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    Homework Helper
    Gold Member

    Your integral is not correct.
    The contribution to the moment of inertia of a mass element, at distance D from the axis, is D2dm. Write up D in terms of r and φ (the polar coordinates. ) You have to integrate for the whole disk.

    ehild
     

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