(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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

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