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Need help quick with rotational acceleration

  1. Jan 7, 2005 #1
    Imagine there is a bicycle wheel. At 1 point on the wheel a rope is fixed to the wheel. The rope is wrapped around the wheel 180 degrees and on the other end of the rope their is a weight (see image below).

    [​IMG]

    The point is actually that I want to compare the weight dropping from different heights (to make the wheel turn) and see which acceleration the wheel gets from these different heights.

    NB: The wheel will only accelerate 180 degrees.

    Please help => HOW??!
     
  2. jcsd
  3. Jan 7, 2005 #2
    Well the tangential force on the weel, exerted by the rope is equal to the gravity force acting on the object. Via [tex]\alpha . R = a_{t} = mgh[/tex] you can calculate the acceleration. Then you can use the formula's for omega (you know [tex]\omega = \omega_{0} + \alpha.t[/tex])and theta in order to calculate the angular velocity omega...alpha is the angular acceleration but you knew that already right ???


    regards
    marlon
     
  4. Jan 7, 2005 #3
    Thanks a lot first of all. Can you please write down a little list: omega = .... alpha = acceleration etc. because I have seen different letters for the same things so I am kind of confused. Thanks.
     
  5. Jan 7, 2005 #4

    omega is angular speed
    alpha is angular velocity
    theta is the angle with the horizotal x-axis.

    [tex]\theta = \theta_{0} + \omega_{0}.t + \alpha . \frac{t^2}{2}[/tex]

    the formula for omega is in my previous post.
    When there is a subscript 0 : it means inital. So inital velocity and theta.

    For eample the [tex]\theta_{0} = \pi[/tex] because you start on the left side of the circle and [tex]\omega_{0} = 0[/tex]

    regards
    marlon
     
  6. Jan 7, 2005 #5
    Thank You!
     
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