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Kleppner & Kolenkow find the tension of a rotating loop of string

  1. Nov 3, 2012 #1
    Hello, I am a high school student trying to learn physics out of Kleppner and Kolenkow. Unfortunately, the solutions to some of the problems are not available online, nor is a solutions manual available, so I am unable to find out where I am wrong in some cases, such as this one. I would appreciate your clarification.

    1. The problem statement, all variables and given/known data
    A piece of string of length L and mass M is fastened into a circular loop and set spinning about the center of a circle with uniform angular velocity ω. Find the tension in the string.


    2. Relevant equations
    The answer in the book states that T = (M*L*ω^2)/(2π)^2, whereas the answer that I got was T = Mω^2/2π.


    3. The attempt at a solution
    Please the attached pdf - I have tried to write as clearly as possible, and am unable to find how my solution is incorrect. Thank you!
     

    Attached Files:

  2. jcsd
  3. Nov 4, 2012 #2

    haruspex

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    A useful check is whether the various items you have expressions for are dimensionally correct. Your final answer has dimensions MT-2, which is wrong for a force.
    Apply the same test to your expression ΔθM/L.
     
  4. Nov 4, 2012 #3
    Thank you! I forgot to include the factor R in there, which gets me where I want to go.
     
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