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What rules are there concerning where to place the origin when calculating center of mass? Take this simple example:

$0.5$ kg and $2.0$ kg, connected by a massless rod $0.5$ m long rod.

By using the common formula $\frac{\sum_i^n m_i\ y_i}{\Sigma m}$ one gets two different results, depending on which of the two masses is chosen as the origin. Specifically $0.40$ m and $0.10$ m. The right choice here is obvious due to common sense, but my textbook doesn't say anything about why. Am I missing something obvious?

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You are missing something obvious. The position you calculate is the position relative to the chosen origin. In one case, it's 40 cm from the lighter mass; in the other case, 10 cm from the heavier mass. Since the two masses (the two chosen origins) were 50 cm apart, that's the same answer...

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See, according to your results, when you took the 0.5 kg mass as origin, the answer was 0.40m. But in the next one, you made a slight mistake. Because it's -0.10m from right(2kg mass). So both the answers are correct. You just have to keep in mind that the distances you put in the equation are relative to the origin you selected.enter image description here enter image description here

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  • $\begingroup$ We have MathJax running in the site so you can typeset mathematics in a LaTeX math-mode alike language. Images if text or mathematics are strongly discouraged. $\endgroup$ – dmckee --- ex-moderator kitten May 6 '17 at 19:35

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