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

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SUMMARY

The center of mass equation utilizes the total mass of the system as the denominator to calculate the weighted average position of all mass components. The formula is defined as x = (m1x1 + m2x2 + ...) / M total, where M total represents the sum of all individual masses. This approach ensures that the center of mass reflects the distribution of mass throughout the entire object rather than just a component. The misconception arises from confusing mass with vector quantities, as mass itself does not have directional components like force.

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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.
 
Last edited:
Mass is also not a vector quantity (it has no components like a force, for instance).
 

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