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Find the angular speed of a cylinder with a spring

  1. Jun 29, 2012 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=48757&stc=1&d=1341010084.gif

    A cylinder of radious r=10cm and mass m=1Kg is attached to a spring of constant k=18N/m.
    In every moment the cylinder rolls without slipping over the inclined plane with an angle of 30º.
    The other extreme of the spring is attached to a fixed point O, as shown. If the cylinder is released from rest being the center of mass a distance L=43cm from point O, ¿which will be the angular speed of the cylinder when its center reaches a distance of L/2 from O?

    The correct answer is 5,1 rad/s.


    2. Relevant equations



    3. The attempt at a solution

    I tried with conservation of energy:

    [tex] \displaystyle {{E}_{0}}=\frac{1}{2}k{{L}^{2}}[/tex]

    [tex] \displaystyle {{E}_{f}}=\frac{1}{2}I\omega +\frac{1}{2}k\frac{{{L}^{2}}}{4}+mg\left( \frac{L}{2}\sin 30{}^\text{o} \right)+\frac{1}{2}m{{v}^{2}}[/tex]

    I have two unknown quantities the angular and linear speed.

    But the angular and linear aceleration are not constant! So how can I figure out the value of V just at point L/2?

    UPDATE: So stupid I am, v=wR and now I do get:

    w = 5.093459858 rad/s :)


    Thanks
     

    Attached Files:

    Last edited: Jun 29, 2012
  2. jcsd
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