- #1
flyingpig
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Homework Statement
Or any coordinates really. In the normal Cartesian plane, the center of mass is defined from the x, y , and z distance as follows[tex]\bar{x} = \frac{1}{Area(R)}\iint_R x dA[/tex]
[tex]\bar{y} = \frac{1}{Area(R)}\iint_R y dA[/tex]
[tex]\bar{z} = \frac{1}{Area(R)}\iint_R z dA[/tex]
Now is there one for polar coordinates where you find the center of mass from the average "r" and "theta"?
[tex]\bar{r} = \frac{1}{Area(R)}\iint_R r dA[/tex]
[tex]\bar{\theta} = \frac{1}{Area(R)}\iint_R \theta dA[/tex]
The Attempt at a Solution
I feel the derivation is going to be a bit lengthy and this really isn't as much of "HW", but just ponder.
In my Calculus book, although we do double integrals in polar coord and find the center of mass, we still stick to the cartesian coordinates.