Timeline for Why does a mass winding up around a cylinder not lose it's velocity?
Current License: CC BY-SA 4.0
14 events
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| Feb 9 at 16:55 | comment | added | Albert | @VedanshTyagi, the assumption that the thread be inextensible implies that at each instant you can picture the thread as a rod, where the rigidity of the rod forces the motion of the disk to be perpendicular to the rod, exactly as it happens in a simple pendulum. In fact, an inextensible thread fixed at one end and attached to a mass at the other end is a compound pendulum with $n$ segments in the limit $n\to \infty$. | |
| Feb 9 at 16:33 | comment | added | Vedansh Tyagi | @Albert This still assumes that the cylinder is only moving along the x axis you defined and not the y axis. If the cylinder moves along the y axis the thread will no longer superimpose the x axis and hence velocity is no longer perpendicular to the force of tension. | |
| Feb 9 at 13:21 | comment | added | Albert | Intuition is also something that increases with practice, @VedanshTyagi. :) That being said, if you want a more intuitive picture, imagine the motion from the point of view of the disk, with planar coordinates where $\hat{y}$ points in the initial direction of the velocity, and $\hat{x}$ in the direction of the thread. From this perspective you would always see momentum pointing upward, the thread lying horizontally, and the cylinder rolling towards the disk as it coils the thread. Clearly, then, the force due to the tension on the thread is always perpendicular to the momentum. | |
| Feb 9 at 11:44 | comment | added | Vedansh Tyagi | Let us continue this discussion in chat. | |
| Feb 9 at 11:36 | comment | added | basics | @VedanshTyagi Here you can find the solution of the problem, from kinematics to the integration of the equation of motion basics.altervista.org/stack-of-notes | |
| Feb 9 at 11:34 | comment | added | Vedansh Tyagi | Sure, thank your for that. | |
| Feb 9 at 11:27 | comment | added | basics | Intuition may be misleading, more times than one would expect. Anyway, when you have an intuition, you need to prove with math | |
| Feb 9 at 11:24 | vote | accept | Vedansh Tyagi | ||
| Feb 9 at 11:21 | comment | added | Vedansh Tyagi | Ok makes sense now. Also did you yourself have the intuition that speed will remain constant at the first glance or did you have to do all the math to get that. | |
| Feb 9 at 11:03 | comment | added | basics | time derivative of the position. How did I come up with position? Kinematic constraints of decreasing free length of the rope ($\ell = \ell_0 - R\theta$, initial free length - length wrapped on the cylinder), along with the condition of straight wire (since massless, this follows from equilibrium of the wire) | |
| Feb 9 at 10:58 | comment | added | Vedansh Tyagi | How did you come up with the expression for the velocity of the particle ? | |
| Feb 9 at 9:38 | history | edited | basics | CC BY-SA 4.0 |
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| Feb 9 at 9:31 | history | edited | basics | CC BY-SA 4.0 |
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| Feb 9 at 9:24 | history | answered | basics | CC BY-SA 4.0 |