Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.

    John
     
  2. jcsd
  3. Aug 1, 2006 #2

    siddharth

    User Avatar
    Homework Helper
    Gold Member

    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

    NateTG

    User Avatar
    Science Advisor
    Homework Helper

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

    HallsofIvy

    User Avatar
    Science Advisor

    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!)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook