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Yo-yo: Vertical acceleration

  1. Dec 7, 2016 #1
    1. The problem statement, all variables and given/known data
    A yo-yo consists of two cylinders with radius ##R##, mass ##M## and height ##H## connected by a smaller cylinder of radius ##r##, mass ##m## and height ##h##.
    Unbenannt.png
    Determine the yo-yo's acceleration in ##z##-direction, using its moment of inertia.

    2. Relevant equations
    Moment of inertia of a solid cylinder: ##I=\frac12mr^2##

    3. The attempt at a solution
    The yo-yo's total moment of inertia is ##I_{\text{tot}}=\frac12mr^2+MR^2##, using the formula for solid cylinders. However, I don't know how to proceed from here.
     
    Last edited: Dec 7, 2016
  2. jcsd
  3. Dec 7, 2016 #2

    TSny

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    Free body diagram.
    ##\sum F = ma##.
    ##\sum \tau = I \alpha##.
     
  4. Dec 7, 2016 #3

    BvU

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    Hi Cep,

    Could gravitational acceleration appear somewhere ?
     
  5. Dec 7, 2016 #4
    I guess so. The acceleration probably consists of both gravitational acceleration downwards and the acceleration upwards caused by the "user" of the yo-yo.
    Is that what you mean?
     
  6. Dec 7, 2016 #5

    BvU

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    Yes. Make a sketch where the driving force acts and how it results in a torque.
     
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