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Polar Co-ordinate intergral

  1. May 22, 2006 #1
    Help! Ive been trying to do this for ages, but i know theres some silly little thing im doing wrong!
    Problem, Find the center of mass of a constant density semicircular plate of radius a, using polar co-ordinates, what regions do i use for the double intergral with respect to r and θ??????
  2. jcsd
  3. May 22, 2006 #2


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    The angle [tex]\theta[/tex] from 0 to [tex]\pi[/tex], and the radius from 0 to a.

    The dA part of the double integration becomes [tex]r dr d \theta[/tex]

    You assume uniform density, so you just intgrating [tex]r\cos\theta[/tex] and [tex]r\sin\theta[/tex] to get the coordinates to the centre of mass.
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