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Center of Mass for 3D Region in Spherical Coordinates
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Description
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Determine  , and  , the center of mass coordinates for a 3D region in spherical coordinates.
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Center of Mass for 3D Region in Spherical Coordinates
( is the colatitude, measured down from the  -axis)
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Density:
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| (1) |
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Region:  <= phi and phi <= phi[2](theta), rho[1](phi, theta) <= rho and rho <= rho[2](phi, theta)}](/support/helpjp/helpview.aspx?si=3999/file05226/math79.png)
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](/support/helpjp/helpview.aspx?si=3999/file05226/math86.png)
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| (2) |
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](/support/helpjp/helpview.aspx?si=3999/file05226/math102.png)
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| (3) |
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](/support/helpjp/helpview.aspx?si=3999/file05226/math118.png)
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](/support/helpjp/helpview.aspx?si=3999/file05226/math134.png)
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| (5) |
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| (6) |
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| (7) |
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Moments ÷ Mass:
Inert Integral - 
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![Student[MultivariateCalculus][CenterOfMass](rho, rho = 0 .. 1, phi = 0 .. (1/6)*Pi, theta = 0 .. 2*Pi, coordinates = spherical[rho, phi, theta], output = integral)](/support/helpjp/helpview.aspx?si=3999/file05226/math191.png)
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| (8) |
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Explicit values for  , and  , the center of mass given in spherical coordinates:
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![Student[MultivariateCalculus][CenterOfMass](rho, rho = 0 .. 1, phi = 0 .. (1/6)*Pi, theta = 0 .. 2*Pi, coordinates = spherical[rho, phi, theta])](/support/helpjp/helpview.aspx?si=3999/file05226/math211.png)
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| (9) |
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