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Rotational Motion Problem - 14

  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-frc3/q71/s720x720/1470127_1461728164054289_845411707_n.jpg

    Attempt -

    https://fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-frc3/q71/s720x720/1468786_1461728244054281_988835356_n.jpg


    Thank you all in advance.
     
  2. jcsd
  3. Dec 17, 2013 #2

    tiny-tim

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    hi coldblood! :smile:

    you're only considering the torque of F (about the centre) … what about the torque of the friction? :confused:

    hint: the clue is in the diagram

    what do you think that dotted line is there for (the extension of F)? :wink:

    what would happen if the angle was larger, and that dotted line went exactly through the bottom of the spool?
     
  4. Dec 17, 2013 #3
    thread unwinds, spool rotates counter-clock and friction would act right wards. Is that correct?
     
  5. Dec 18, 2013 #4

    tiny-tim

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    (just got up :zzz:)
    (ie if the force goes exactly through the point of contact with the horizontal surface)
    nooo (and what was your reason?) :redface:

    hint: where is the centre of rotation?

    what is the total torque about the centre of rotation? :wink:
     
  6. Dec 18, 2013 #5
    If the external force acts at the bottom point horizontally,

    It'll provide spool an anti clockwise torque, friction will act leftwards. And I think thread should unwind.

    Because I found some equations: if the force acts at the top point horizontally in + x direction, It generates a torque in clockwise manner and direction of friction is rightwards.
     
  7. Dec 18, 2013 #6

    tiny-tim

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    no, you're not understanding what i'm saying …

    i'm saying, if the angle α is increased so that the pulling force F is further round, and steeper, and so the line of action of F (as well as f) goes through that bottom point
     
  8. Dec 18, 2013 #7
    Then the spool will be rotating clockwise, friction will act right right and thread unwinds.
     
  9. Dec 18, 2013 #8

    tiny-tim

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    ??

    how many forces are there on the spool?

    what is the torque of each of them about the bottom point?

    so what is the total torque?
     
  10. Dec 18, 2013 #9
    About bottom point only the torque of F will act because weight, frictional force and the reaction from the ground will pass through that point only.
     
  11. Dec 18, 2013 #10

    tiny-tim

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    exactly! :smile:

    so if the line of action of F passes
    (a) to the left of
    (b) to the right of
    (c) directly through​
    the bottom point, which way will the spool turn? :wink:
     
  12. Dec 18, 2013 #11
    Can you please make a figure for the three? Please
     
  13. Dec 18, 2013 #12

    tiny-tim

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    (a) is the diagram in the top-left corner of your printed question

    for (b) and (c), if you move the string further round, α will increase, and the dotted line will slide over to the right

    (eg if α = 90°, it's obviously to the right!)
     
  14. Dec 19, 2013 #13
    https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-prn2/1476572_1462877957272643_1028005643_n.jpg
    https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-prn1/q71/s720x720/936643_1462877960605976_1351577648_n.jpg
     
  15. Dec 19, 2013 #14

    tiny-tim

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    hi coldblood! :smile:

    your first equation, α = F(b - a)/IP is correct only if the angle of F is 0

    you have drawn F in the wrong place, F does not come out of the bottom of that small circle, it has to be tangential, so it comes from a point at the same angle from the vertical as F is from the horizontal :wink:

    and you do not really need to calculate it exactly, or to use k

    it's enough to say "the only torque about P is from F, which is clearly clockwise, and so the spool rotates clockwise" :smile:

    similarly, the only torques about C are F (anticlockwise) and f … since we know the spool rotates clockwise, that means that the torques of f must be … ? :smile:

    now do the other two cases, (b) and (c) (with a corrected diagram)​
     
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