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Homework Help: Angular acceleration & cylinder

  1. Nov 6, 2005 #1
    M, a solid cylinder (M=1.59 kg, R=0.127 m) pivots on a thin, fixed, frictionless bearing. A string wrapped around the cylinder pulls downward with a force F which equals the weight of a 0.750 kg mass, i.e., F = 7.357 N. Calculate the angular acceleration of the cylinder.
    I used,
    I*alpha= mgr
    (1/2)mr^2 *alpha= mgr
    (1/2)(1.59)(.127)^2 * alpha= (1.59)(9.8)(.127)
    Solving for alpha gave me 155.9 rad/s^2
    which wasn't right. Can someone help? Thanks.
     
  2. jcsd
  3. Nov 6, 2005 #2

    lightgrav

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    Did you forget the "rotational Inertia" of the hanging mass?
    Include the .75 kg mass at the R^2 where the string joins.

    Otherwise, you have to use the Tension in the string, rather than mg,
    to provide torque on the disk. (with mg - T causing ma of the hanger).
     
  4. Nov 6, 2005 #3
    so would I do..
    (1/2)(1.59+ .75)(.127)^2 * alpha= (1.59)(9.8)(.127)

    I'm a little confused about where the .75 comes into it
     
  5. Nov 6, 2005 #4

    lightgrav

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    Inertias add.
    IF you actually HAVE a hanging mass on the string you'd do
    I_total = I_disk + I_hanger = (1/2)(1.59)(.127)^2 + (.75)(.127)^2 .

    But the wording in the problem is peculiar, you might NOT have a hanger.

    You somehow used the weight of the cylinder (rather than 7.36 N) to provide the torque which is supposed to angularly accelerate the cylinder.
    Sorry I hadn't noticed it before, the wording is really distracting.
     
  6. Nov 7, 2005 #5
    Ok I figured out what I was doing wrong and got the right answer.. it was 72.9 rad/s^2.
    The second part says if instead of the force F an actual mass m= .750 kg is hung from the string, find the angular acceleration of the cylinder. I got this part it was 37.5 rad/s^2.
    The third question says how far does m travel downward between 0.530 s and 0.730 s after the motion begins?

    I used a= delta w/delta t
    37.5= delta w/ .2
    delta w= 7.5 rad/s
    then, delta w= delta theta/ delta t
    7.5= delta theta/ .2
    so theta =1.5 m
    this isn't right.
    Can someone help me? Thanks.
     
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