Center of Mass Formula

  • Thread starter eprparadox
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Main Question or Discussion Point

Hello,

I'm reading Mathematical Methods in the physical sciences by Mary Boas and in it, she defines the center of mass of a body in 3 dimensions

[tex] \int \overline {x}dM=\int xdM [/tex]

[tex] \int \overline {y}dM=\int ydM [/tex]

[tex] \int \overline {z}dM=\int zdM [/tex]

In standard undergraduate textbooks, I've always seen it written as

[tex] \overline {X}=\dfrac {1} {M}\int xdM [/tex]

I guess I don't understand the reasoning behind defining it the way she did. I know that [tex]\overline {x} [/tex] is constant so you can pull it out and you'd just simply get the [tex] \int dM [/tex], leaving you with the formula that is generally seen in undergraduate texts.

But why write the formula as she did to begin with. Is there a particular benefit to doing so?


Any insight would be great, thanks.
 

Answers and Replies

  • #2
Khashishi
Science Advisor
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No, there's no benefit to writing it that way. Different style, I guess.
 
  • #3
clem
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Her way is more 'mathematical', which makes her book awkward.
 
  • #4
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I think the advantage is that Boas' form gives the center of mass for any volume in a system, rather than only giving the center of mass for the entire system. For example, when considering the earth-moon system, we might want to calculate the center of mass of the moon and not the center of mass of the system--so you take your volume of integration around just the moon subset of the system, and you get the center of mass for just the subsystem. I guess you could do it like the style of Griffiths E&M and call it Menclosed but Boas' definition automatically clears up that ambiguity.
 
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