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This is the identity given in my textbook with regards to the centre of mass of of a set of particles along the line. $x$ could be the distance along the line, and $y$ could be the mass. $\sum x_i y_i$ would then be the sum of moments of forces.

Mihail
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1 Answers1

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This is the definition of the centre of mass; more specifically, the centre of mass $\bar x$ is defined in this context by $$ \bar x = \bigg( \sum x_i y_i \bigg) \bigg/ \sum y_i $$ (the horizontal moment divided by the mass).

Greg Martin
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  • Ah I see. A confusing notation that clashes with statistics, where $\bar{x} = \frac{1}{n}\sum x_i$. – Mihail Sep 26 '19 at 15:47
  • If it helps, think of this formula as a generalization of the one from statistics, where all the "particles" (measurements) have the same mass $y_i=1$. – Greg Martin Sep 26 '19 at 20:01