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Spherical Coordinates and Centre of Mass

  • Thread starter JaysFan31
  • Start date
  • #1
JaysFan31
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
 

Answers and Replies

  • #2
siddharth
Homework Helper
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You need to show your work before you get help. What are your thoughts/ideas on this problem?
 
  • #3
JaysFan31
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?
 
  • #4
NateTG
Science Advisor
Homework Helper
2,450
5
Well, what happens if the density is 1 (with appropriate units)?
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
41,794
925
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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