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Rotational Motion Problem - 11

  1. Dec 16, 2013 #1
    Hi friends,
    Please help me in solving this problem, I'll appreciate the help.

    The problem is as:

    https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-prn2/q71/s720x720/1503374_1461728057387633_909744247_n.jpg

    Attempt -

    https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-prn2/1506899_1461728417387597_658199054_n.jpg



    Thank you all in advance.
     
  2. jcsd
  3. Dec 16, 2013 #2

    haruspex

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    a = Rα is for rolling contact.
     
  4. Dec 17, 2013 #3
    Yes But centre of mass of the sphere woild be going with Translational acceleration,
    Whose value would come from the bottom point in contact using, a = rα
    Isn't it?
     
  5. Dec 17, 2013 #4

    haruspex

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    No, as I said, that's only for rolling contact. When the spinning cylinder is placed on the plank it will skid at first. Suppose frictional force is F. What linear acceleration will that produce? What torque? What angular acceleration?
     
  6. Dec 17, 2013 #5
    https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-ash4/1506955_1462163254010780_1540770628_n.jpg
     
  7. Dec 17, 2013 #6

    haruspex

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    That's all correct, but what you are asked for is a. Your remaining step is to figure out what f is in terms of m, g and mu.
     
  8. Dec 17, 2013 #7
    Well, here a is f/m and f will be, μmg/m = µg(i)
    and acceleration of plank would be µg(-i)

    so acceleration of sphere w.r.t. plank would be 2µg.

    Is that correct?
     
  9. Dec 18, 2013 #8

    haruspex

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    That's it. You didn't need to worry about the rotations at all!
     
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