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Centroid of a circular segment

  1. May 4, 2013 #1
    1. The problem statement, all variables and given/known data

    I need to find the centroid of a circular segment. I know nothing of calculus, and this is part of an analysis for statics that goes beyond the material covered in class.


    2. Relevant equations

    I've seen this equation for calculating the centroid:

    [itex]\bar{y}[/itex]=[itex]\frac{4Rsin^3\frac{\theta}{2}}{3(\theta-sin\theta)}[/itex]

    Please the Wiki link for the diagram:
    http://en.wikipedia.org/wiki/File:Circularsegment_centroid.svg


    3. The attempt at a solution

    For a circle of 1 inch diameter, with an angle of 60°:

    4(0.5")sin(30)^3= 0.25

    divided by:

    3(60-sin60)≈ 177.4

    Answer: approximately 0.001"

    Surely the centroid should be within the segment? Separately, I've found the centroid of a semicircle using:

    [itex]\bar{y}[/itex]=[itex]\frac{4R}{3\pi}[/itex]

    which gave reasonable results. I'm led to believe the first equation should give the correct centroid position for a semicircle (θ=180°), but I also got a very small distance for that, too.

    What am I missing about the first equation?

    Thanks.


    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 4, 2013 #2
    θ should be expressed in radians. 60 degrees is π/3 radians.
     
  4. May 4, 2013 #3
    Very gently stated. :)

    Thanks, Chester!
     
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