(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

We have a rigid body that is formed by two coaxial cylinders, one with radius [tex]r[/tex] and another with radius [tex]R[/tex], [tex]r < R[/tex]. There's a winding of string around the cylinder of smaller radius. The string is pulled with a constant force [tex]F[/tex] making an angle [tex]\alpha[/tex] with the horizontal.

There is no "sliding", only rotation.

What is the "critical" angle [tex]\alpha[/tex] for which the direction of the movement changes?

2. Relevant equations

[tex]\vec{F} = m \vec{a}[/tex]

[tex]\tau = \vec{F} \times \vec{r}[/tex]

[tex]\tau = I \vec{\vec{\ddot{\theta}}}[/tex]

3. The attempt at a solution

Well, at first I was a bit skeptical since I couldn't quite imagine pulling the string to one side and the cylinder coming to that side. I thought that pulling the string to one side would make the cylinder rotate away always. So, I made the experiment and the direction of the movement did in fact change with the angle.

I've been thinking and I could only conjecture one thing: when I'm pulling the string with an angle, I can not assume that the force is being applied to the lowest point, yielding a torque [tex]\tau = F r \cos \alpha[/tex], instead I should think that the string is always perpendicular to [tex]\vec{r}[/tex], and that the net torque is [tex]\tau = F r[/tex]. But this lead me nowhere.

Can you help me? I don't want a solution, I just want a little help to "see the physics" of the problem.

Regards

Krappy

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# Cylinder Rotating

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