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Math Help - Spherical Coordinates and Centre of Mass

  1. #1
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    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
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  2. #2
    Grand Panjandrum
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    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
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  3. #3
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    Could someone just help me set up the integrations for the x centre of mass?
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  4. #4
    Grand Panjandrum
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    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:

    <br />
\bold{R}=\frac{1}{M} \int_V \rho(\bold{r})\ \bold{r} dV<br />

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

    RonL
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