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Angular acceleration for one gear to another

  1. Oct 2, 2015 #1
    1. The problem statement, all variables and given/known data
    vsubV.png
    Gear r has angular acceleration of a magnitude of .2 rads^{-2}(counterclockwise) and is resting at t=0s . p is a cylinder welded to R (concentric). r applies torque to R, these do not slip or slide. A mass m hangs from a string which is attached to p. This string is not elastic nor does it have mass. The gears and cylinder are massless, and the mass has no effect on the acceleration of the gears.
    r=5cm ; R=20cm ; p=10cm ; acceleration of r =.2 rads^{-2}

    a) Find distance travelled by m after 10 seconds (t=10s)
    b) Find velocity of m at said postion (t=10s)
    2. Relevant equations
    w=v/r ; radians travelled = .5(Ang. Accel.)t^2 (omitting initial conditions) ; radians = d/r ;
    w=(ang. acc.)t (omitting initial conditions)

    3. The attempt at a solution

    I'd much rather not go through the tedious task of rewriting all my work in a format I am not accustomed to. You can see all the above information in another forum where I posted the same question. For the sake of time, here is http://physics.stackexchange.com/questions/209973/how-do-you-find-the-longitude-travelled-by-a-string-hooked-to-a-concentric-cylin?noredirect=1#comment449514_209973 [Broken] and formatted.
    Although I managed to acquire what seemed like reasonable answers, they differ to the answer key's ( a. d=83.3cm b. v=25cm/s)
    I got 25cm for m's displacement and 5 cm/s velocity.
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Oct 2, 2015 #2

    gneill

    User Avatar

    Staff: Mentor

    Your results look fine to me. Perhaps the problem's given values were tinkered with to "refresh" the question, while the answer key was not updated.

    You could take a screen snip of your work and post the image to conform to our rules that you must show your work:
    MyWork.PNG
     
  4. Oct 5, 2015 #3
    Alright, I´ll take your word for it. I had been suspecting this for some time now. Thank you so much.
     
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