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Rotational Dynamics: Pulley and mass system

  1. Jan 2, 2014 #1
    1. The problem statement, all variables and given/known data
    A 8.0-cm radius disk with a rotational inertia of 0.12 kg*m^2 is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end. The mass is raised by a using a crank to apply a 9.0-N*m torque to the disk. The acceleration of the mass is:
    A. 0.50 m/s^2
    B. 1.7 m/s^2
    C. 6.2 m/s^2
    D. 12 m/s^2
    E. 20 m/s^2
    Answer: A

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


    3. The attempt at a solution
    The net torque of the system is:
    I*[itex]\alpha[/itex] = I*a/r = 9.0 N*m - [itex]F_{T}[/itex]*r
    Thus, [itex]F_{T}[/itex] = (Ia/r-9)/(-r)
    By N2L:
    ma = [itex]F_{T}[/itex] - mg = (Ia/r-9)/(-r) - mg
    Rearranging gives:
    a = (mg)/((I/r-9/(-r))-m) and substituting in values gives me an answer of about 1.17 m/s^2.

    Can someone direct me on where I have gone wrong in my calculations? I would very much appreciate it :)
     
    Last edited: Jan 2, 2014
  2. jcsd
  3. Jan 2, 2014 #2
    Open up the RHS and carefully collect the terms containing a.
     
  4. Jan 2, 2014 #3
    Ok thank you. I guess my mistake was just in bad algebra :P
     
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