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How much is the angular acceleration?

  1. Jun 18, 2012 #1
    1. The problem statement, all variables and given/known data

    289fuq1.jpg

    the mass, M, of the disk is 20kg, the radius is r and the force applied, F, in the periphery of the disk is 9.8N. How much is the angular acceleration?

    If I add a mass (m1) of 1kg to the thread what will be the angular acceleration?

    2nr1r9s.jpg

    2. Relevant equations

    I think those are relevant to my problem:
    Moment of inertia of a disk: I=0.5*m*r^2
    Torque=Force*radius*sin(tetha)
    angular acceleration=Torque/Moment of inertia


    3. The attempt at a solution

    a) I=.5mr^2 ⇔I=2.5
    Torque=9.8*0.5=4.9N*m
    angular acceleration=4.9/2.5 = 1.96 rad/s^2

    I think this one is correct

    b) Since it was added another mass I tought that the total force would be F+T, tension being equal to the force of the mass*gravity (9.8). Then:
    I=2.5
    Torque=9.8N*m
    angular acceleration=9.8/2.5=3.92 rad/s^2

    The correct answer is 1.8 rad/s^2. any hints would be highly appreciated!

    Thanks.
    D.
     
  2. jcsd
  3. Jun 18, 2012 #2
    b) There are 2 objects to be accelerated. The mass and the wheel.
     
  4. Jun 18, 2012 #3
    I forgot to mention the wheel is fixed.

    D.
     
  5. Jun 18, 2012 #4
    The mass has translational acceleration, the wheel has rotational acceleration.
    The system has 2 objects, a wheel and a mass.
    The system is now supplied with 2 forces.

    For the first question, only one object and a single force applied.
     
    Last edited: Jun 18, 2012
  6. Jun 18, 2012 #5
    Thank you very much!
     
  7. Jun 18, 2012 #6

    ehild

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    Homework Helper
    Gold Member

    It is meant that you attach a mass of 1 kg to the cord, instead of applying the force of 9.8 N. The tension in the cord acts at the rim of the disk. the difference of gravity and tension accelerates the hanging object.

    ehild
     
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