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A yo-yo pulled by a rope: limit angle for the yo-yo to go to the left or to the right

  1. Jan 18, 2012 #1
    1. The problem statement, all variables and given/known data
    We have a yo-yo, formed by a little cylinder tied to a little rope, and two big disks as wheels, one for each side of the central cylinder. We do a force T on the rope; its slope is an angle θ over the horizontal x-axis.
    We are given the mass m of the cylinder, the mass M of each wheel, the radius of the cylinder R1 and the radius of each wheel R2. We want to know the limit angle θ , for the acceleration to be positive or negative.
    I try to explain it better: under a certain angle, the yo-yo have a pure roll in the positive direction, over this angle it goes "back" and rolls towards the negative direction.


    3. The attempt at a solution
    I put in all the forces, the weight $mg$, the reaction $N$, and the friction force (static, since it's roling) towards the left side.
    My equations are:
    T*sinθ + N = m*g
    T*cosθ - f[itex]_{s}[/itex] = m*a[itex]_{cm}[/itex]
    f[itex]_{s}[/itex]*R2 - T*R1 = I[itex]_{G}[/itex]*α = I[itex]_{G}[/itex] * a[itex]_{cm}[/itex] / R2

    But I'm always obtaining a non-sense answer solving the system, I guess I'm doing wrong something about the signes. Can someone help me?
    Thanks a lot.
     
  2. jcsd
  3. Jan 18, 2012 #2

    lightgrav

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    Re: A yo-yo pulled by a rope: limit angle for the yo-yo to go to the left or to the r

    when it rolls, its rotation is around the point where it contacts the ground.
    If the torque around this point is zero, it does not roll (alpha = 0).
     
  4. Jan 18, 2012 #3
    Re: A yo-yo pulled by a rope: limit angle for the yo-yo to go to the left or to the r

    Thank you very much| Now I got it :D
     
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