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Center of mass

  1. Nov 23, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the center of mass of a semicircular wire. The wire is a semicircle, but the important thing to realize is that the wire is a closed loop. Think of a solid half disk, and just take the outer edge.
    Where is the center of mass? This will be positioned with the center at the origin.
    Radius b.

    2. Relevant equations
    cm = x1*m+x2*m/total mass

    3. The attempt at a solution
    What I tried to do was try to stay away from the integrals since there are just wires being used.
    For the center of mass of x, it will be at zero because of symmetry.

    For y, I used the equation above. With uniform density, the mass will factor out and I will just be left with lengths.

    (2b*0 + Pi*b*2*b/Pi )/(2b + Pi*b)... is this right? or would you suggest that I use integrals.
    Last edited by a moderator: Nov 23, 2013
  2. jcsd
  3. Nov 23, 2013 #2


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    Gold Member

    Self-contradictory. Doesn't make sense. Draw a picture.
  4. Nov 23, 2013 #3
    Here is the picture!

    Attached Files:

    • nng.gif
      File size:
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  5. Nov 23, 2013 #4


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    Gold Member

    That makes sense. The wire is not a semi-circle, it is a semi-circle AND a connecting wire.
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