1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the center of mass of an incomplete circle

  1. May 21, 2013 #1
    1. The problem statement, all variables and given/known data

    Locate the x coordinate of the center of mass of the homogeneous rod bent into the shape of a circular arc. Take r = 170 .

    The arc goes from (-5/6) to (5/6)pi (counterclockwise). It has a radius of 170mm.


    2. Relevant equations

    x=rcosθ, y=rsinθ, dL=r*dθ


    3. The attempt at a solution

    I found "M" by integrating "170 dθ" from (-5/6)pi to (5/6)pi. This gave me 890.12mm.


    I found "My" by integrating "170 (cosθ) 170 dθ" from (-5/6)pi to (5/6)pi. This gave me 170^2 or 28900mm.

    I used My/M to find the x coordinate of the center of mass as 28900/890.12 or 32.468mm. However this is incorrect.
     
    Last edited: May 22, 2013
  2. jcsd
  3. May 21, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The solution looks good, but you miss the unit, and try to give the result with three significant digits.

    ehild
     
  4. May 22, 2013 #3
    I updated the units. I also found out that the answer is supposed to be 70.3mm but I still can't figure out how to get that.
     
  5. May 22, 2013 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Are the limits -5/6 and 5/6pi, or -5/6pi and 5/6pi? But even then, the result is different from that 70 mm. The given results happen to be wrong quite often.

    ehild
     
  6. May 22, 2013 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    That would be the answer if the angle were -2π/3 to +2π/3.
     
  7. May 22, 2013 #6

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You are a genius! So they took over the solution from an old version of the problem, while changing the limits in the problem text. :biggrin:

    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding the center of mass of an incomplete circle
  1. Find center of mass (Replies: 1)

Loading...