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Homework Help: Center of Mass via Scalar Line Integrals

  1. Mar 30, 2010 #1
    1. The problem statement, all variables and given/known data
    A thin wire has the shape of the first quadrant part of the circle with center at the origin and radius a. If the density function is rho(x,y)=kxy, find the mass and center of mass of the wire.

    2. Relevant equations
    My parametric equation of the circle was x=a*cos(t) and y=a*sin(t).

    3. The attempt at a solution
    I really have no clue where to begin for finding the center of mass of the wire. I think I got the mass via integral(k*a^2*sin(t)*cos(t) dt = -(k*a^2)/2. Thanks for the help!
  2. jcsd
  3. Mar 30, 2010 #2


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    Hi Hashmeer! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    No, mass = ∫ density*d(length),

    and d(length) is not dt, it's … ? :smile:
  4. Mar 30, 2010 #3
    Yea, I looked over my notes and I figured out what I need to do. Thanks for confirming what I was thinking was wrong.
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