Why Is Total Mass Used as the Denominator in the Center of Mass Equation?

AI Thread Summary
The center of mass equation uses total mass as the denominator to calculate a weighted average of the positions of all mass components in a system. This approach ensures that each mass contributes proportionally to its position, reflecting the overall distribution of mass. The suggestion to use a component-specific total mass misinterprets the nature of mass as a scalar quantity rather than a vector. Understanding that mass does not have directional components clarifies why the total mass of the system is appropriate for the calculation. The equation effectively represents the balance point of the entire mass distribution.
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so for the center of mass of an object..

x = (m1x1 + m2x2 + ...) / M total
y = (m1y1 + m2y2 + ...) / M total

how come in this equation the denominator is the total mass of the system? It seems like it would make more sense to have the denominator the total mass in whatever component you are trying to figure out...

i feel like it should be
x = (m1x1 + m2x2 + ...) / Mx total

and though i realize this is wrong i was hoping somebody could see what i think i see and explain where my thinking is wrong.
 
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Simply put, it's a weighted average.
 
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Mass is also not a vector quantity (it has no components like a force, for instance).
 
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