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Simple Harmonic Motion with Rotational Inertia

  1. Aug 28, 2016 #1
    1. The problem statement, all variables and given/known data
    One end of a light spring with force constant k = 100 N/m is attached to a vertical wall. A light string is tied to the other end of the horizontal spring. the string changes from horizontal to vertical as it passes over a pulley of mass M in the shape of a solid disk of radius R = 2.00 cm. The
    pulley is free to turn on a fixed, smooth axle. The vertical section of the string supports an object of mass m = 200 g. The string does not slip at its contact with the pulley. The object is pulled downward a small distance and released.

    (a) What is the angular
    frequency v of oscillation
    of the object in terms of
    the mass M?

    (b)What
    is the highest possible
    value of the angular frequency
    of oscillation of the object?

    2. Relevant equations


    w=(k/m)exp1/2

    3. The attempt at a solution
    I honestly do not know where to start... For a), wouldn't you simply use the w=(k/m)exp1/2 formula since the angular frequency only depends on the mass and the spring contsant?
     
    Last edited: Aug 28, 2016
  2. jcsd
  3. Aug 29, 2016 #2

    ehild

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    Do you think that the mass of the pulley does not affect the angular frequency?
     
  4. Aug 29, 2016 #3
    In the problem, it stated that the pulley had a mass M with Radius = 2.00cm so I am assuming the mass of the pulley does matter, which lead me to thinking that the mass used in the w=(k/m)exp1/2 equation is in fact m = mass of object + mass of pulley.

    I tried finding the mass of the pulley using the moment of inertia formula before realizing that I'd actually need the pulley mass for that too..
     
  5. Aug 29, 2016 #4

    ehild

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    The mass of the pulley does matter. It is M which can have different values. Solve the problem in terms of M and k. Write the acceleration of m with the forces acting on it and the angular acceleration of M with the angular momenta of the forces acting on it. What are those forces?
     
  6. Aug 29, 2016 #5
    What would I use to find the M mass of the pulley? I've tried moment of inertia and that doesn't work because you need the mass for I=MR^2.
     
  7. Aug 29, 2016 #6

    ehild

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    You can not find M. It is arbitrary. Find the frequency in terms of M.
     
  8. Aug 29, 2016 #7

    ehild

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    Draw the free-body diagram for m and M. What forces act on m, and at the rim of the disk? How is the acceleration of m related to these forces? How is the angular acceleration of the disk related to the torque of the forces acting at its rim?
    upload_2016-8-29_14-49-8.png
     
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