Center Of Mass Deriving

  • Thread starter Dweirdo
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  • #1
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OMG second time I'm opening a thread in the wrong forum FFS!!!!
Damn bookmarks!! MODS move it please.

Homework Statement


Not a home work question, just something i cam across and need a clarification.
Could One show me how to derive to the equation that X(cm)=int(X dm)/M
int=the deformed S of the integral(2 lazy to write in Latex XD).


Homework Equations


X(cm)=sigma(Xi Dmi)/M

The Attempt at a Solution


I know It's simple, But I can't imagine how sigma(Xi Dmi) becomes int(X dm),
I don't understand what it means , trying to convert it to words just doesn't work for me,so could some 1 explain that for me?
AFAIK sigma(Xi Dmi) means the mass distribution,but how does the integral takes place here?
I really need to understand the math part in physics.

Thanks a lot in advanced !
 
Last edited:

Answers and Replies

  • #2
tiny-tim
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Hi Dweirdo! :smile:

(have a sigma: ∑ and a delta: ∆ and an integral: ∫ and try using the X2 tag just above the Reply box :wink:)
… I can't imagine how sigma(Xi Dmi) becomes int(X dm),
I don't understand what it means , trying to convert it to words just doesn't work for me,so could some 1 explain that for me?
AFAIK sigma(Xi Dmi) means the mass distribution,but how does the integral takes place here?
How does ∑ Xi ∆mi become ∫ X dm ?

Because that's what an ∫ is …

it's defined as the limit of a ∑ as the ∆s tend to zero. :smile:
 
  • #3
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Hi Dweirdo! :smile:

(have a sigma: ∑ and a delta: ∆ and an integral: ∫ and try using the X2 tag just above the Reply box :wink:)


How does ∑ Xi ∆mi become ∫ X dm ?

Because that's what an ∫ is …

it's defined as the limit of a ∑ as the ∆s tend to zero. :smile:
But why?? Like I know that in Energy, if you make a graph of force and distance and it is curved than integral calculates the plot.
but wtf is it here?
thanks :}
 
  • #4
tiny-tim
Science Advisor
Homework Helper
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Because energy (= work done ) = force x distance, so it's the limit of ∑ (force x ∆distance)

Similarly, moment of mass = distance x mass, so it's the limit of ∑ (distance x ∆mass) :smile:
 

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