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Rolling without slipping, theory

  1. May 6, 2017 #1
    1. The problem statement, all variables and given/known data
    I am solving a question that asks for, what's the minimum coefficient of friction required for a cylinder to roll without slipping? Where the cylinder has a force F acting on its center.
    upload_2017-5-6_19-1-53.png


    2. Relevant equations
    upload_2017-5-6_18-58-1.png
    And
    upload_2017-5-6_18-58-31.png

    3. The attempt at a solution
    From the way I understand it, the only torque acting on the cylinder is the torque from friction, since the torque from force F is acting at the center, thus resulting in 0 torque.

    But the resource I'm looking at assumes that torque from friction is not the only torque acting on the cylinder. But it doesn't explain why.

    Where are the other torques acting from?
     
    Last edited: May 6, 2017
  2. jcsd
  3. May 6, 2017 #2

    BvU

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    Your problem statement may be incomplete. Zero is the answer as it is written now.
     
  4. May 6, 2017 #3
    Oops! Yeah I changed it.
     
  5. May 6, 2017 #4

    BvU

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    Tell us what you see. Our telepathic capabilities are limited.

    And: what do you do with the given 'rolling without slipping' ?
     
  6. May 6, 2017 #5
    http://www.feynmanlectures.info/solutions/roll_without_slipping_sol_1.pdf
    On step 6, it says, "In order for the ball not to slip, the torque on the ball from friction can not be less than the total torque on the ball when it rolls"
    (Note: I tweaked the problem from a slope to a flat ground for simplification purposes, so I don't have to worry about the theta for now)

    Well since it is rolling without slipping, the linear acceleration must equal to angular acceleration multiplied by radius:
    upload_2017-5-6_19-37-21.png

    So since the sum of torques is the torque from friction:
    upload_2017-5-6_19-43-13.png

    Is this correct then?

    (Sorry about the really big pictures)
     

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  7. May 6, 2017 #6

    haruspex

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    Retry that last step.
    Also, your answer should express μmin in terms of F, M, g and R (or any subset of those).
     
  8. May 6, 2017 #7
    upload_2017-5-6_19-49-45.png

    :doh:
     
  9. May 6, 2017 #8

    haruspex

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  10. May 6, 2017 #9
    Hm..

    The only substitution which I can make is this:
    upload_2017-5-6_20-11-35.png

    I am not sure how to get R in there.
    It seems that the coefficient of fric. is not dependent on R.

    Interesting, this follows:

    upload_2017-5-6_20-17-9.png
     
  11. May 6, 2017 #10

    haruspex

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    No, acm is not F/M.
    As I wrote, a subset of those variables is fine. It just must not involve any variables outside of the given set.
     
  12. May 7, 2017 #11
    Oops! acm is net force / m,

    upload_2017-5-7_11-30-26.png
     

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  13. May 7, 2017 #12

    haruspex

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