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Barrel roll with/without slipping

  1. Aug 17, 2013 #1
    Hi guys,

    I'm wondering if I roll a barrel which rolls without slipping down an inclined plane vs. a barrel which only slips down the plane - who will get down faster and how can I show it mathematically ?


    Thanks
     
  2. jcsd
  3. Aug 17, 2013 #2

    Doc Al

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    Staff: Mentor

    Start by drawing free body diagrams for each situation. Then you can calculate the acceleration.
     
  4. Aug 17, 2013 #3

    bgq

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    Do what Doc Al have told you, the final result is that the barrel that slips down falls faster than the one that rolls.
     
  5. Aug 17, 2013 #4
    For rolling without slip:
    mgh=0.5Iω + 0.5mV^2, I=0.5MR^2 ->
    mgh=0.25mR^2 * (V/R)^2 +0.5MV^2
    gh=0.25V^2 + 0.5V^2 ->
    V=√4/3 gh

    For slip only:
    mgh=0.5mV^2 ->
    V=√2gh

    and so the Velocity at the bottom of the inclined plane is higher for slip only. is that correct?
     
  6. Aug 17, 2013 #5

    Doc Al

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    That's correct. (I see you modeled the barrel as a solid cylinder, which is OK.)
     
  7. Aug 17, 2013 #6
    Thank you for the help! much appreciated
     
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