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Homework Help: Centre of mass

  1. Oct 6, 2008 #1
    1. The problem statement, all variables and given/known data
    Center of Mass of a hemisphere

    http://www.goiit.com/templates/default/images/chapters/center_mass/image064.gif [Broken]
    http://www.goiit.com/templates/default/images/chapters/center_mass/image068.gif [Broken]
    Why is volume of elemental disc = [tex]Rd\theta (cos \theta) (\pi R^{2}cos^{2} \theta)[/tex] and not

    [tex]Rd\theta (\pi R^{2}cos^{2}\theta)?[/tex]
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Oct 7, 2008 #2


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    Because the arc length is measured from the [itex]\theta=0[/itex] plane (yz plane) to the plane rotated through an angle [itex]d\theta[/itex], So the radius of the arc is the projection of R onto the [itex]\theta=0[/itex] plane which is [itex]Rcos(\theta)[/itex] and so the arc length is [itex]Rcos(\theta)d\theta[/itex].
  4. Oct 7, 2008 #3
    I dont get it. Could you please take some of ur precious time out, just to draw a very rough sketch in paint? Please!!
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