centroid of a plane area

Discussion in 'Physics' started by logearav, Feb 22, 2012.

  1. logearav

    Thread Starter Member

    Aug 19, 2011
    248
    0
    Revered members,
    Please look at my attachment. I need to find the centroid of the plane area. The radius of semi circle at the bottom and top is 3 cm. I dont know how to proceed. Should i use the formula for semicircle or semi ellipse? Help in this regard will be greatly appreciated.
    In fact i have no clue as to how to proceed. Please help
     
  2. MrChips

    Moderator

    Oct 2, 2009
    12,449
    3,364
    Have you done integration as yet?
     
    logearav likes this.
  3. logearav

    Thread Starter Member

    Aug 19, 2011
    248
    0
    I know integration. Just guide me how to proceed Mrchips. Thanks for your reply
     
  4. MrChips

    Moderator

    Oct 2, 2009
    12,449
    3,364
    The centroid (or center of mass) along one axis is the sum of each point mass multiplied by its distance from a reference point, then divided by the sum of each point mass.

    You can express this as:

    \overline{x} = \frac{\sum{mx}}{\sum{m}}

    The first step would be to find the centroid of a semi-circle.

    Do you know how to calculate the area of a circle using integrals knowing the formula for circumference?

    circumference = 2\pi r

    If so, calculate the centroid of a semi-circle by dividing the semi-circle into small half rings going out from the center of the circle.
     
    Last edited: Feb 23, 2012
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