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Homework Help: Mastering Physics: Acceleration of a Pulley

  1. Apr 15, 2017 #1
    1. The problem statement, all variables and given/known data
    A string is wrapped around a uniform solid cylinder of radius r, as shown in (Figure 1) . The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m.
    Find the magnitude α of the angular acceleration of the cylinder as the block descends.
    upload_2017-4-15_19-12-53.png

    2. Relevant equations
    F=ma=mg-T
    Torque=Iα=-Tr
    a=-rα
    I=mr2/2
    3. The attempt at a solution
    I use these three equations to eliminate T and solve for α.

    m(-rα)=mg-T
    -1/2mr=T
    -mrα=mg+1/2mr
    -α=g/r+1/2
    α=-1/2-g/r

    I tried this answer however it was wrong.

    Mastering says the correct answer is
    α = 2g/3r

    I'm really not sure where this comes from, so any help would be great! I need to understand where I went wrong.
     
  2. jcsd
  3. Apr 15, 2017 #2
    Where did this come from? It doesn't look right.

    Edit: Okay, now I see what you did. You were equating Iα to -Tr, then substituting I = mr2/2 for I. You should work through that algebra again and I think you'll find your problem.
     
  4. Apr 15, 2017 #3
    I dropped the g. Thank you so much! I found the correct answer.
     
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