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Confused about pulleys and tension

  1. Nov 5, 2013 #1
    Sometimes when I see pulley and rope questions people will say "for a non-extensible rope the tension is uniform throughout the rope". But I am now learning pulleys and rotational inertia and it seems to be necessary to consider the rope on either side of a pulley to have _different_ tension if the pulley is being accelerated rotationally.

    Why would this different tension not apply to a frictionless massless pulley that is being accelerated rotationally?

    For example, here we see the rope have different tension on each side of the pulley:

     
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Nov 5, 2013 #2

    Doc Al

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    The key word is massless. A massless pulley requires no net torque to rotationally accelerate, thus the tension must be the same on each side. (Actually, frictionless is important too! If there were friction, you'd need a net torque to overcome it.)
     
  4. Nov 5, 2013 #3
    To be clear, the different torques are used when the pulley requires torque, but NOT simply because the pulley accelerates rotationally, correct?
     
  5. Nov 5, 2013 #4

    haruspex

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    Yes.
     
  6. Nov 8, 2013 #5
    I meant different TENSIONS, of course, not different torques.

    Thanks haruspex!
     
  7. Nov 8, 2013 #6

    haruspex

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    Actually, it can happen that torques are the same but the tensions are different. The pulley's axis could be off-centre.
     
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