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Torque on a Cylinder

  1. Oct 22, 2016 #1
    1. The problem statement, all variables and given/known data

    A cylinder having a mass of 5.0 kg can rotate about its central axis through point O. Forces are applied as shown in the figure: F1 = 5.0 N, F2 = 6.0 N, F3 = 2.5 N, and F4 = 5.5 N. Also, R1 = 6.5 cm and R2 = 12.0 cm. Find the magnitude and direction of the angular acceleration of the cylinder. (Take clockwise to be +.) (During the rotation, the forces maintain their same angles relative to the cylinder.)

    phys fig.jpg

    2. Relevant equations
    τ=I⋅α=r⋅F⋅sinΦ
    Icyl = ½MR2

    3. The attempt at a solution
    So I started with
    τnet=F2⋅R1 - F1⋅R2 + F4⋅0
    and τ=Iα , so F2+R1 - F1⋅R2=Iα.
    Substituting in I:
    F2⋅R1 - F1⋅R2=½MR2α
    Solved for α to get
    2[F2⋅R1 - F1⋅R2 ]/MR2
    Plugging and chugging I got:
    2[(6.0N-5.0N)(0.12m)+(2.5N)(0.065m)]/(5.0kg)(0.12m)2
    α=0.94 rad/s2

    But this isn't correct. Can you help me figure out what I'm doing wrong? Thanks!
     
  2. jcsd
  3. Oct 22, 2016 #2
    I didn't work all the way through your solution (I don't have much time right now), but your original τnet equation has errors. You should carefully go through that.
     
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