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Center of Mass for 3-D Region in Cylindrical Coordinates
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Description
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Determine  ,  , and  , the center of mass coordinates for a 3-D region in cylindrical coordinates.
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Center of Mass for 3-D Region in Cylindrical Coordinates
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Density:
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| (1) |
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Region:  <= r and r <= r[2](theta), z[1](r, theta) <= z and z <= z[2](r, theta)}](/support/helpjp/helpview.aspx?si=3998/file05225/math73.png)
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](/support/helpjp/helpview.aspx?si=3998/file05225/math80.png)
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](/support/helpjp/helpview.aspx?si=3998/file05225/math97.png)
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](/support/helpjp/helpview.aspx?si=3998/file05225/math113.png)
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](/support/helpjp/helpview.aspx?si=3998/file05225/math129.png)
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| (7) |
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Moments ÷ Mass:
Inert Integral - 
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![Student[MultivariateCalculus][CenterOfMass](__z__, z = __r__ .. 1, r = 0 .. 1, theta = 0 .. (1/3)*Pi, coordinates = cylindrical[r, theta, z], output = integral)](/support/helpjp/helpview.aspx?si=3998/file05225/math191.png)
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| (8) |
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Explicit values for  ,  , and  , the center of mass given in cylindrical coordinates:
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![Student[MultivariateCalculus][CenterOfMass](__z__, z = __r__ .. 1, r = 0 .. 1, theta = 0 .. (1/3)*Pi, coordinates = cylindrical[r, theta, z])](/support/helpjp/helpview.aspx?si=3998/file05225/math213.png)
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| (9) |
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