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Yoyo problem

  1. Nov 4, 2008 #1
    1. The problem statement, all variables and given/known data

    The string in a yo-yo is wound around an axle of radius 0.512 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.206 kg and outer radius 1.88 cm. Starting from rest, it rotates and falls a distance of 1.20 m (the length of the string). Assume for simplicity that the yo-yo is a uniform circular disk and that the string is thin compared to the radius of the axle. What is the speed of the yo-yo when it reaches the distance of 1.20 m? How long does it take to fall?

    2. Relevant equations

    mgh=1/2mv^2+1/2Iw^2
    I=1/2mr^2
    w=v/r

    3. The attempt at a solution

    r1=.512
    r2=1.88
    mgh=1/2mv^2+1/2(1/2mr2^2)(v/r2)^2

    The answer is obviously incorrect. What exactly am I doing wrong? Thanks!
     
  2. jcsd
  3. Nov 5, 2008 #2

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper

    You're almost there, there's just a small change to make in your equation.

    w depends on the radius at which the string is located.

    The string isn't wound around the outside of the yo-yo (r2 that you used in w=v/r), so think about where the string is wound on the yo-yo.

    p.s. welcome to PF.
     
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