# Spherical Coordinates and Centre of Mass

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

Related Calculus and Beyond Homework Help News on Phys.org
siddharth
Homework Helper
Gold Member
You need to show your work before you get help. What are your thoughts/ideas on this problem?

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?

NateTG
Science Advisor
Homework Helper
Well, what happens if the density is 1 (with appropriate units)?

HallsofIvy
Science Advisor
Homework Helper
You will also need to know that the "differential of volume" in spherical coordinates is
$$\rho^2 sin(\phi)d\rho d\theta d\phi$$
(I'm sure that's in your text book!)