# Spherical Coordinates and Centre of Mass

• Aug 1st 2006, 09:05 AM
JaysFan31
Spherical Coordinates and Centre of Mass
Wondering if someone could help me get this answer. I don't get spherical coordinates at all. What does the uniform material part mean in terms of delta?

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
• Aug 1st 2006, 09:35 AM
CaptainBlack
Quote:

Originally Posted by JaysFan31
Wondering if someone could help me get this answer. I don't get spherical coordinates at all. What does the uniform material part mean in terms of delta?

It means that the density is constant - that is it is independent of position.

RonL
• Aug 1st 2006, 07:17 PM
JaysFan31
Could someone just help me set up the integrations for the x centre of mass?
• Aug 1st 2006, 08:09 PM
CaptainBlack
Quote:

Originally Posted by JaysFan31
Could someone just help me set up the integrations for the x centre of mass?

You know that the centre of mass is defined by:

$\displaystyle \bold{R}=\frac{1}{M} \int_V \rho(\bold{r})\ \bold{r} dV$

where $\displaystyle V$ is the volume occupied by the mass, $\displaystyle M$ is the total mass, and $\displaystyle \rho(\bold{r})$ is the is the density at point $\displaystyle \bold{r}$.

RonL