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Kinematics question(angular velocity)

  1. Dec 6, 2017 #1
    1. The problem statement, all variables and given/known data
    Question: A circular cylinder with mass of 1 kg and radius a=0.1 m is rotating about its cylindrical axis at a rate of 5 revolutions per second. It is then placed on a flat surface. Assuming that there is no dissipation at contact and the cylinder is rolling without slipping (with negligible rolling friction) on the flat surface, its translational speed is:

    2. Relevant equations
    v=rω

    3. The attempt at a solution
    v=0.1 (5*2π)=π m/s

    The answer is 1.81m/s. Can anyone help?
     
  2. jcsd
  3. Dec 6, 2017 #2

    PeroK

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    You've answered a different question. The question you have answered was:

    If a cylinder is rolling without slipping at 5 rev/s then what is its translational speed.

    That said, I'm not sure what the question is asking. If you put the spinning cylinder on a surface, then there must be energy loss before it gets to a state of rolling without slipping. But, the question seems to ask you to ignore this energy loss. Perhaps try that?
     
  4. Dec 6, 2017 #3

    PeroK

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    You've assumed that the cylinder has translational speed before it is placed on the surface.
     
  5. Dec 6, 2017 #4
    how can I answer this question? The rotational kinetic energy is conserved.
    1/2mv2=1/2Iω2
    If I put the data into this equation, v=2.22m/s . I still can't get the answer.
     
  6. Dec 6, 2017 #5

    PeroK

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    Now you have assumed that the cylinder has stopped rotating and has only translational motion. Note that:

    Initially the cylinder is rotating

    Finally it is rolling without slipping
     
  7. Dec 6, 2017 #6
    How can I calculate the final angular velocity? Is the final angular velocity=v/r?
     
    Last edited: Dec 6, 2017
  8. Dec 6, 2017 #7
    I think I have got the correct approach.
    1/2 I ωi2=1/2mv2+1/2 I ωf2
    v=√1/3r2ωi2
     
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