Recent content by ricles

feels like I was a blind for not seeing it 😅 thanks! also, thanks Steve for the resources ^^

Oh, but wouldn't you have a chain to be close enough to an elastic band if the chain's links were small enough? Or, even if they weren't, wouldn't the links not hit the ground flat and lose their KE if they were rotating fast enough (due to inertia)?

I'm not sure I follow you. Do you refer to the tension calculated as ##\frac{mR\omega^2}{2\pi}##? Then it doesn't quite seem to be independent of R 🤔 (we have ## \frac{mR\omega^2}{2\pi} = \frac{mR\left(\frac{v}{R}\right)^2}{2\pi} = \frac{mv^2}{2\pi R} ##, which does seem to depend on R, right...

Yes, that's right. It's actually not complicated after thinking a little, we have (##a_k## denoting the acceleration at the point k): $$ \begin{align} a_{cm} & = \frac{f}{m_1 + m_2} \\ \tau &= f\cdot R = I\cdot \alpha = \left(\frac12 m_1 R^2 \right) \alpha \therefore \alpha = \frac{2f}{m_1R} \\...

This comes from a list of exercises, and setting ##m_1 = 5.4kg##, ##m_2 = 9.3kg## and ##F=5N##, the answer should yield ##2.19m/s^2## (of course, supposing the answer is right). If I knew the radius ##R## of the cylinder, I could find its momentum and use it to find the linear acceleration...

(maybe) Interestingly, my next question (that I wouldn't post here, but since you alluded to it) would be: now, if there was a pump on the road, and the chain went rotating over it the pump would generate a pulse that propagates through the chain. What would be the velocity of the propagating...

But then, being impossible doesn't stop people from considering things like perfect circles, that rotate while having only one point in contact with the floor - and that could still provide useful results. I agree, considering the situation presented, ##\frac{mR\omega^2}{2\pi}## is a good...

Thanks a lot for the reference! Indeed, the problem seems more complicated in general. But, in principle, shouldn't you be able to rotate the chain (or ribbon, or what have you) quickly enough so that it doesn't deform/collapse after you let it go, for at least some time? Maybe it will deform...

it doesn't spontaneously, but yet it is thusly put in motion - you can picture yourself rotating a short light chain with your fingers and letting it go on the floor, for instance, and in principle you should be able to rotate it fast enough that it doesn't collapse when you let it go. but I'm...

I know the solution for the problem of the tension on a rotating ring without gravity (tha is, ##\frac{mR\omega^2}{2\pi}##) - that I find simple enough. But I'm at a loss how can I change it to do with gravity :/ Any help is appreciated! (and apologies for the bad drawing)