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How to find centre of gravity for a hemisphere shell?

  1. May 3, 2005 #1
    How to find centre of gravity for a hemisphere shell??

    Can someone show me how to calculate centre of gravity for a hemisphere shell??
     
  2. jcsd
  3. May 3, 2005 #2

    SpaceTiger

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    These sound suspiciously like homework problems.
     
  4. May 4, 2005 #3
    It's not homework, I'm preparing for an examination. And I have serious problem solving this assignment. Pleas help me!!
     
  5. May 4, 2005 #4
    Integrate mass density over the surface for each axial direction. As far as I can remember for rectangular coordinates its

    [tex] y_{cm} = \int{\rho(x) f(x)dx} [/tex]

    [tex] x_{cm} = \int{\rho(x) xf(x)dx} [/tex]

    but my memory is probably mistaking me. There should be an example of this in your book though.
     
  6. May 4, 2005 #5

    dextercioby

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    Here's the hint:use the rotation around Oz symmetry to transform your problem into a very simple one:finding the C of M for a semicircle of radius R.You basically need the "z" coordinate of the C of M for the hemisphere,or the "y" coordinate for the C of M for the semicircle.

    Daniel.
     
  7. Sep 7, 2008 #6
    Re: How to find centre of gravity for a hemisphere shell??

    The result obtained from integration and your symmetry argument are NOT the same.
    For a semicircular wire, the COM is [tex](0, \frac{2R}{\pi})[/tex] while from integration, it is [tex](0,0,R/2)[/tex]. Can anybody explain this?
     
  8. Dec 24, 2011 #7
    Re: How to find centre of gravity for a hemisphere shell??

    I know this is an old post, but I have been struggling with the same problem for a while now , can anyone explain this?
     
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