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For example, if I draw a line on the side of a pencil top to bottom, then snap one end of it as in launching it due to the pressure of my fingers. Anyways, if I record the pencil launch in slow motion (perhaps it’s my phone that has to do with it) but it will focus on where the line was, and it appears that only some of the actual line is there, or out of focus. So that leads to the question, does rotation happen simultaneously down the pencil axis? Maybe I’m completely clueless and I’m missing something but figured I’d ask.

LanceCantSkate
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No, the rotation would not occur instantaneously. When you flick one end of the pencil, the molecules (at the end) you imparted an impulse to will have gained momentum and would pull the molecules just beside them due to internal electrostatic forces holding the molecules together, (much like the propogation of a mechanical wave) and bring them to motion and this cascading effect will keep travelling down the pencil.

TL;DR, it will not be instantaneous and will take a small finite time that is usually negligible.

Chaitanya Gambali
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  • In other words, you can't move a stick stick many light-years long back and forth for faster than light communications. – DKNguyen May 25 '21 at 18:53
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In general for a rigid body you have the combined motion of translation of the center of mass and rotation about the center of mass at any instant.

The COM moves with $\boldsymbol{v}_C$ and the body rotates (simultaneously) with $\boldsymbol{\omega}$.

So the motion of any other point P, located at $\boldsymbol{r}$ relative to the center of mass is

$$ \boldsymbol{v}_P = \boldsymbol{v}_C + \boldsymbol{\omega} \times \boldsymbol{r} $$

The particulars on how much translation vs. rotation happens depend on the situation. This is the area of kinematics, where constraints on rigid bodies only allow a certain subset of the motions that a body would normally have.

JAlex
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Your question is a bit difficult to understand,but what you seem to be saying is that if you launch your pencil like a dart & give it some spin as you launch it,will the rotation manifest itself instantaneously along the whole length of the pencil? No,it won't. No signal can travel faster than light,so the rotation imparted to the middle of the pencil by your fingers will travel to the ends of the pencil at speed c,but as the speed of c is 300,000K (186,000 miles)per sec & your pencil is perhaps 10" long,the rotation will appear to be simultaneous along the entire length of the pencil.

Michael Walsby
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    Why do you think the rotation will propagate along the pencil at the speed of light? Mechanical vibrations generally travel much slower than that. – PM 2Ring May 28 '19 at 01:42
  • Because the pencil is too rigid for it to propagate at any other speed..If pencils were made out of rubber it might propagate at a leser speed,but they're not. If you bang a nail into a block of wood,there is a brief interval betrween the hammer striking the head & the movement of the sharp end into the wood,because the force takes time at speed c to travel from hammer to sharp end,though it appears to be instantaneous.. – Michael Walsby May 28 '19 at 10:51
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    No, when the hammer strikes the head of the nail, the pulse propagates through the nail at the speed of sound, which is a little under 6000 m/s for a steel nail. See https://physics.stackexchange.com/q/21122/123208 and the linked & related questions. – PM 2Ring May 28 '19 at 12:23
  • There may be a sound wave passing through the nail at whatever the speed of sound is in steel.,but the actual force of the hammer striking the nail will be transmitted at speed c. The speed of sound is very slow by comparison. If your nail could be 100 miles long,the sound would arrive a measurable interval after the tip had moved. . – Michael Walsby May 28 '19 at 12:41
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    @MichaelWalsby I don't see a problem with a 100 mile long nail having the force hit the other end only seconds later. That "slow" speed is still a lot faster than you're going to be able to process unless you are very high above, and have some large enough visual indicator of the force propagation to even notice. Also, why would it propagate at the speed of light in a vacuum while travelling through a nail? – JMac May 28 '19 at 13:59
  • 100-mile long nail is a thought experiment,because it's not practical in real life. Perhaps a steel bar about 10 metres long would suffice if you had instrumentation sensitive enough to measure the time difference between arrival of the sound wave & the movement of the far end of the bar. Re the vacuum,it is not light which propagates through the steel bar but the influence of the electromagnetic force as countless negatively charged electrons push against & repel each other. Maybe you're right,& the speed of transmission would be less than c,but I'm pretty sure it would be faster than sound. – Michael Walsby May 28 '19 at 14:32
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    @MichaelWalsby Have you done any research at all into it though? Do you have any solid justification for being pretty sure that it will travel faster than the speed of sound? Consider it this way, the speed of sound is how fast a pressure wave travels in a medium. When force is transferred through an object, that is also done as a pressure wave. Why would you expect it to propagate any faster than the limit for pressure waves in that medium? – JMac May 28 '19 at 16:29
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    Consider that sound is the transfer of mechanical disturbance from one part on a medium to other parts. That is, the speed of sound is defined as the speed at which mechanical disturbances propagate. – dmckee --- ex-moderator kitten May 28 '19 at 21:25