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Homework Help: The yo-yo

  1. Oct 11, 2009 #1
    1. The problem statement, all variables and given/known data
    A yo-yo is made from two uniform disks, each with mass m and radius R, connected by a light axle of radius b. A light, thin string is wound several times around the axle and then held stationary while the yo-yo is released from rest, dropping as the string unwinds. Find the linear acceleration of the yo-yo.

    2. Relevant equations


    3. The attempt at a solution


    since [itex]a_{tan}=r\alpha[/itex],substituted into the equation above and simplified,

    Tb=mRa[/itex] ...1

    The yo-yo is accelerating downwards linearly, so

    2mg-T=2ma[/itex] ...2

    Solving for T in eq.1 and substituting into eq.2,


    Solving for a, I got


    which is not the right answer... the correct answer is

    what did I do wrong??
  2. jcsd
  3. Oct 11, 2009 #2


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    Homework Helper

    Hi kudoushinichi88! :smile:

    (I haven't actually checked your equations, but …)

    wouldn't it be easier to use conservation of energy? :wink:
  4. Oct 11, 2009 #3


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    Homework Helper

    String unwinds around the cylinder of radius b. So a(tan) = b
  5. Oct 11, 2009 #4
    You substituted the wrong value for r. If the yoyo unwinds with angular speed [tex]\omega[/tex]
    the vertical speed of the yoyo is [tex]b \omega[/tex] and not [tex]R \omega[/tex]
  6. Oct 13, 2009 #5
    ah... so that's why!
    Thank you all! This has also helped me to find the angular acceleration and tension in the string...
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