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Cylinder rolling down an inclined plane

  1. Mar 12, 2012 #1
    This is an even-numbered problem in my textbook that I'm looking at early though it hasn't been taught by my lecturer yet, because I need to know the concepts underlying it for a similar problem. Cld someone help me?

    1. The problem statement, all variables and given/known data

    Consider the case of a hollow cylinder rolling down a plane inclined to the ground at an angle β. There is a small piece of plasticine stuck to a fixed position on the cylinder's inner circumference. What is the acceleration in this case?

    Assume the small piece of plasticine to be a rigid cylinder of radius r and mass m, and the hollow cylinder to be of radius R and mass M.

    2. Relevant equations

    The formula for acceleration of hollow and filled cylinders

    3. The attempt at a solution

    Can't solve...


    Help please?


    Thanks!
     
  2. jcsd
  3. Mar 13, 2012 #2
    i'm not too sure but i'm throwing it out there.

    (whenever i type "I" it's for moment of inertia, when talking about myself i'll use lower case i).
    i assume you need first to find the moment of inertia through the center of the body, then use Steiner's equation to find I on the edge that is touching the incline.
    The hardest part here is that I of the edge that is touching the incline changes according the where the plasticine is, so you would have to find I as a function of θ (angular position of the plasticine).
    and θ is a function of how the body rolls.
    if it's rolling without slipping you can do a moment equation on the edge of the body
    Ʃτ=Iα
    α=a/R
    and maybe throw in a force equation or two, i think you should reach a good equation with θ and it's derivatives...
    hope this helped.
     
    Last edited: Mar 13, 2012
  4. Mar 13, 2012 #3
    Thanks. But i know these already.

    By the way, there is friction, which has nonzero torque on the centre of the can.
     
  5. Mar 13, 2012 #4
    Could you be more specific and show how you did the maths?

    Sorry I'm so amateur-ish
     
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