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If the x location of the centroid equals (moment about O)/(equivalent point weight) and there are forces acting above and below the given body, couldn't the value of the x coordinate potentially extend beyond the body?

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  • $\begingroup$ I don't really follow the wording of this. You can definitely have a centroid (or center of mass) that is outside of the physical body, if that's what you're asking. $\endgroup$ – JMac Oct 10 '19 at 19:03
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    $\begingroup$ take a donut, the center of Mass will not be in the donation, but in the hole $\endgroup$ – trula Oct 10 '19 at 21:15
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Yes. What you are doing with $ x=\frac{M_O}{W} $ is finding the moment arm of the weight. That is typically the center of mass of a body.

Reverse the equation to get $M_O = x W$, or the moment about origin depends on the moment arm of the weight $W$.

Now the part of your question that compares this $x$ with the "extent of the body" it is unclear, although logic dictates that the center of mass is always within the bounds of a solid body.

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