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Boas Mathematical physics book, definition of center of mass

  1. Jul 5, 2011 #1

    fluidistic

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    In Boas' book I can read that the definition of center of mass of a body has coordinates [itex]x_{CM}= \int x_{CM}dM= \int x dM[/itex].
    Shouldn't it be this same integral but divided by M?!
    Also, I didn't find the definition of center of mass for particles or any non continuous bodies.
    I'd be grateful if someone could point me what I'm missing.

    Edit: I forgot to say it's on page 210 in the 2nd edition.
     
    Last edited: Jul 6, 2011
  2. jcsd
  3. Jul 6, 2011 #2
    How could this be true? The second equality is correct. Since x_CM is a constant, you can pull it out of your integral. There's your missing M. You'll thus have x_CM = integral(stuff)/M

    For discrete objects, it is just a weighted mean of the positions. Should be in there somewhere!
     
  4. Jul 6, 2011 #3

    fluidistic

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    My bad, I misunderstood the book. The first equality is wrong and the second is right as you said. Now I get it. Thanks a lot.
    Yeah I know how to calculate the center of mass of discrete objects. I just wanted to be sure and refered to the book but couldn't find it (still didn't find it).
     
  5. Jul 6, 2011 #4
    If that is so, then simply substitute in the density of the object delta functions for those mass points and the continuous reduces to the discrete ;)
     
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