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Kinetic energy of a segment

  1. Dec 28, 2012 #1
    1. The problem statement, all variables and given/known data
    (see attachment 1)


    2. Relevant equations



    3. The attempt at a solution
    I have attached my working, the correct answer is (A) but I can't see where I went wrong.

    Any help is appreciated!
     

    Attached Files:

  2. jcsd
  3. Dec 28, 2012 #2

    haruspex

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    Your first line is wrong. How did you get 1+sin(θ)? You're measuring it down fron horizontal, so should be minus.
    And in the last step, you've evaluated the integral of the sin(θ) part to zero. It won't be.

    Another approach is to say the angular speed is v/R and work out the distance from the element to the point of contact.
     
  4. Dec 28, 2012 #3
    Oh yes, the integral sin(θ) won't be zero. I evaluated it correctly during the examination but did it wrong while posting up my attempt. :tongue2:
    I did the necessary corrections as you said and got the right answer. One more question, would the limits for integration change from 0 to -pi?

    This approach is much easier. I am not much familiar with the instantaneous axis of rotation but this worked out pretty well. Thanks for the alternate method. :smile:
     
  5. Dec 28, 2012 #4

    haruspex

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    No, you're measuring theta anticlockwise in the diagram from the "9 o'clock" position, so it will be 0 to pi.
     
  6. Dec 28, 2012 #5
    Got it, thanks haruspex!
     
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