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X coordinate

  1. Feb 23, 2004 #1
    A baseball bat of length 1.05 cetimeters has a lenear density given by l=.950 + 1.050x^2/l^2 find the x cooridinate of the center of mass in centimeters.

    How am I supposed to work this problem?
  2. jcsd
  3. Feb 23, 2004 #2
    Center of mass is a weighted average. Each part's contribution, all other things being equal, increases proportional to distance from the origin as one moves away from the origin. Just combine "average" and "weighted" to get:

    [tex]\overline{x} = \frac{\int^a_bx\lambda(x)dx}{\int^a_b\lambda(x)dx}[/tex]

    where [a,b] is the region describing the bat (0 to 1.05 in your case) and [itex]\lambda(x)[/itex] is the linear density function in terms of x. You'll notice that the top half of the fraction is the "weighted" part, which you're dividing by the total mass to get the "average" part.

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