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Rotational Dynamics: Net Torques

  1. Jan 2, 2014 #1
    1. The problem statement, all variables and given/known data
    RotationalMotion_3.png
    Answer: C

    Note: Sorry admins for the picture, needed to include the diagram though.

    2. Relevant equations
    ∑[itex]\tau[/itex] = I[itex]\alpha[/itex]
    ∑F = ma
    a = [itex]\alpha[/itex]r


    3. The attempt at a solution
    The torques must be balanced (is this reasoning already wrong?), thus,
    F*R1 = F_T*R2
    F_T = FR1/R2
    The only force acting on the block is the F_T, thus the acceleration is FR1/mR2

    Why are the torques not balanced in this case? If not, how do I exactly relate the moment of inertia of the entire disk to fit into the entire problem? Thank you in advance for the help!
     
    Last edited: Jan 2, 2014
  2. jcsd
  3. Jan 2, 2014 #2

    tiny-tim

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    hi henryli78! :smile:
    yes, the torques are balanced only if α = 0 :wink:
     
  4. Jan 2, 2014 #3
    Thank you! I solved it.

    I wrote out:
    Net Torque = I*alpha = I*a/R2 = F*R1 - T*R2
    T = ma, thus I*a/R2 = F*R1 - m*a*R2
    I*a/R2 + m*a*R2 = F*R1
    a(I/R2+mR2) = F*R1
    a(I + mR2^2) = F*R1*R2
    a = F*R1*R2/(I+mR2^2)

    Thank you very much for the help :)
     
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