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Spherical Coordinates and Centre of Mass

  1. Aug 1, 2006 #1
    Wondering if someone could help me get this answer. I don't get spherical coordinates at all.

    The volume of the region given in spherical coordinates by the inequalities
    3 less than or equal to rho less than or equal to 5
    0 less than or equal to phi less than or equal to pi/6
    -pi/6 less than or equal to theta less than or equal to pi/6
    is filled with uniform material. Find the x-coordinate of the centre of mass.

    Thanks for any help.

  2. jcsd
  3. Aug 1, 2006 #2


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    You need to show your work before you get help. What are your thoughts/ideas on this problem?
  4. Aug 1, 2006 #3
    Ok. I know that the centre of mass is the triple integration of density x-bar over just the triple integration of the mass. I guess I don't know what the density function is. I'm pretty sure that x=rhosin(phi)cos(theta).

    I'll integrate with the given bounds. But what is the density function?
  5. Aug 1, 2006 #4


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    Well, what happens if the density is 1 (with appropriate units)?
  6. Aug 2, 2006 #5


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    You will also need to know that the "differential of volume" in spherical coordinates is
    [tex]\rho^2 sin(\phi)d\rho d\theta d\phi[/tex]
    (I'm sure that's in your text book!)
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