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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.

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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.

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  • $\begingroup$ In other words, you can't move a stick stick many light-years long back and forth for faster than light communications. $\endgroup$
    – DKNguyen
    May 25 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.

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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.

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    $\begingroup$ Why do you think the rotation will propagate along the pencil at the speed of light? Mechanical vibrations generally travel much slower than that. $\endgroup$
    – PM 2Ring
    May 28 '19 at 1:42
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    $\begingroup$ 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 physics.stackexchange.com/q/21122/123208 and the linked & related questions. $\endgroup$
    – PM 2Ring
    May 28 '19 at 12:23
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    $\begingroup$ @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? $\endgroup$
    – JMac
    May 28 '19 at 13:59
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    $\begingroup$ @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? $\endgroup$
    – JMac
    May 28 '19 at 16:29
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    $\begingroup$ 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. $\endgroup$ May 28 '19 at 21:25

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