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How to devise moment of inertia formula of solid sphere?

  1. Oct 24, 2015 #1
    1. The problem statement, all variables and given/known data
    how to devide moment of inertia of solid sphere about its central axis?. Solid sphere has radius R, mass M.

    2. Relevant equations

    I=∫r2dm
    2/5 MR^2
    3. The attempt at a solution
    https://photos.google.com/search/_tra_/photo/AF1QipPoXyad0q1Y3yisc0LeeJHGApkIrGbitK6kAk5p
    i try to imagine that solid sphere is a group of infinite disk. a disk have volume dv=πr2dx.
    dm=ρdv=πρr2dx.
    I=R-Rr2πρr2dx
    I=πρR-Rr4dx
    I=πρR-R(R2-x2)2dx
    I=πρR-RR4-2R2x2+x4dx
    I=πρ[2R5-4/3R5+2/5R5]
    !=πρR5[30-20+6]/15
    I=16/15 πρR5
    I=4/5 (4/3πρR3)R2
    I=4/5MR2

    where my eror? i have spent 2 days to solve it but i am failed until now.
     

    Attached Files:

  2. jcsd
  3. Oct 24, 2015 #2

    haruspex

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    In your first integral, you introduce an extra factor r2. I assume this is related to the moment of inertia of a disk about its axis. Have you forgotten something there?
     
  4. Oct 24, 2015 #3
    i think this is just subtitution for dm=ρπr2dx. i'm confused
     
  5. Oct 24, 2015 #4

    haruspex

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    No, in the next line you have another r2 factor.
     
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