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Center Of Mass Deriving

  1. Apr 20, 2009 #1
    OMG second time I'm opening a thread in the wrong forum FFS!!!!
    Damn bookmarks!! MODS move it please.
    1. The problem statement, all variables and given/known data
    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).


    2. Relevant equations
    X(cm)=sigma(Xi Dmi)/M

    3. 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: Apr 20, 2009
  2. jcsd
  3. Apr 20, 2009 #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:)
    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:
     
  4. Apr 21, 2009 #3
    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 :}
     
  5. Apr 21, 2009 #4

    tiny-tim

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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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