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Final angular velocity of a mass on a pulley

  1. Nov 15, 2011 #1
    1. The problem statement, all variables and given/known data
    Use Newton's 2nd Law, sum of torques, and kinematic equations to determine the angular speed of the spool shown in the figure below. Assume the string has a negligible mass, and it turns without slipping. Use g=10 m/s2 for acceleration due to gravity.
    1dzor5.png


    2. Relevant equations
    Ʃτ=rxF=Iα
    F=mA
    ωf2i2+2αΔθ

    3. The attempt at a solution
    Sum of torques:
    Ʃτ=rxf
    =(.6m)(3kg*10m/s2)(sin 90°)=Iα
    --> 18 kgm2/s2=Iα
    α=18/[.5(5)(.62)]
    α=20 rad/s2

    But plugging this into the kinematic equation to solve for ωf doesn't give me the right answer (I know this because I calculated ωf based on conservation of energy first (ωf=11.01 rad/sec), so I think I may have messed up somewhere up until this point. Any suggestions?
     
  2. jcsd
  3. Nov 15, 2011 #2

    Doc Al

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    Staff: Mentor

    Do not assume that the force exerted on the spool equals the weight of the bucket. You need to figure out the tension in the string. (Analyze forces on the bucket as well as on the spool.)
     
  4. Nov 15, 2011 #3
    Thank you! I knew it was something having to do with the tension. And I wasn't thinking of doing forces on both objects, more of just doing it as a whole.
     
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