Rotate Pencil About Axis AB: What Obs. C Sees

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Discussion Overview

The discussion revolves around the effects of rotating a pencil about an axis in a hypothetical scenario where the pencil is two light-seconds long and situated in outer space, away from gravitational influences. Participants explore the implications of this rotation from the perspectives of observers A, B, and C, particularly focusing on the transmission of kinetic energy and the resulting mechanical behavior of the pencil.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that observer A can rotate the pencil, but the motion at B will not occur until at least 2 seconds later due to the distance involved.
  • Others argue that the pencil will twist rather than rotate rigidly, as there are no truly rigid objects in relativity.
  • One participant suggests that the pencil may break instead of twisting, depending on the force applied and the speed of rotation.
  • Another participant mentions that the speed at which kinetic energy travels along the pencil is likely much slower than the speed of light, possibly comparable to the speed of sound in the material of the pencil.
  • Some participants discuss the implications of stress and strain on the pencil, questioning whether the stress would exceed normal twisting limits.
  • There is a suggestion that the speed of stress transmission depends on the material properties, such as mass-density and Young's modulus.
  • Participants explore the possibility of measuring the velocity of kinetic energy transmission across the pencil, considering factors like RPM, circumference, and material properties.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the pencil will break or twist, with multiple competing views on the mechanical behavior of the pencil under rotation. The discussion remains unresolved regarding the exact outcomes of the scenario.

Contextual Notes

Limitations include assumptions about the material properties of the pencil, the nature of forces applied, and the effects of relativistic mechanics on the behavior of the pencil during rotation.

Who May Find This Useful

This discussion may be of interest to those studying mechanics, relativity, or material science, particularly in understanding the implications of motion and stress in extended objects.

Yaaks
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I have a Simple question,
What will happen when i rotate a Pencil about the axis AB as in fig.

A ---------------------------------------------B
|
|
|
C
Let,
* The Pencil be in outer space, away from any gravitational influence.
* The Pencil be two Ly.sec long.

'C' is a neutral observer who is equi-distant from observer A and observer B so that light from A and B will have to travel a dist. 'd ' before reaching C.

Let obs. A rotate the Pencil about the axis AB.
Qs) 1>Will obs. A be able to Rotate the axis AB?, since the Kinetic Energy generated at End A will take more than 2 Secs to travel to B because AB is two ly.sec long and nothing can travel faster than light.
2>What will obs. 'C' note down about the event at A and B and what will he conclude?. (Imagine You being observer 'C'.)
 
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C is the mid-point of AB, Plz ignore the typing error...
Thanx
 
Assuming that the only force applied to the pencil is applied at A, then you are right that no motion can occur at B until at least 2 secs later. The pencil will twist. There are no such things as rigid objects in relativity.

As C is the same distance from A and B, he or she will see A move first and then B move at least 2 secs later.
 
wht i figured was that the pencil would break rather than twist...or maybe A would not be able to rotate the pencil at all...
 
Whether it breaks or not depends how much force you apply and how quickly.
 
....Assuming tht the force generated @ A travels along AB @ the speed of light?
 
No, more nearly the speed of sound in whatever material the pencil is made of. The stresses travel along the pencil by way of intermolecular forces, like sound waves do.
 
The pencil will break. Mechanical waves travel much slower than 'c'. Major league baseball players can break bats merely by swinging them.
 
Last edited:
Why will the pencil break? Although on a large scale the pencil will appear twisted, at any given point along the pencil I'd think the stress would not be any greater than it is along a normal pencil when you twist it.
 
  • #10
The Pencil has to break, given the fact tht its 2 lysec long and the twist generated @ A will take a resonably long time to reach B...and i don't think the pencil will be flexible enough to twist a full 360 deg.
@Chronos,, Does the speed @ which the KE is transferred depend upon the mass-density function of the pencil...
 
  • #11
Yaaks said:
The Pencil has to break, given the fact tht its 2 lysec long and the twist generated @ A will take a resonably long time to reach B...and i don't think the pencil will be flexible enough to twist a full 360 deg.
It depends on how fast you twist it at A.
Example: Assuming that the twist travels at the speed of sound through the pencil, and you take 1 sec to rotate A 360 degrees, then the front end of the twist will be 330 meters down the pencil by the time you finish your 360 deg rotation at A. The pencil will be twisted 360 degrees over a length of 330 meters, or just a little over 1 deg per meter. I was able to twist an ordinary pencil better than 1 deg over its length(much less than 1 meter) without it breaking, so this should be no problem. (If the twist travels at the speed of light then you are talking about a 360 deg twist stretched out over a length of 3,000,000 meters)
 
  • #12
ok..
1>Is it possible to measure the vel. @ which the KE travels across AB?,
given,
The RPM for that twist, the circumference of that Pencil (imagining it to be round), the mass-density function (lets take an Iron Rod instead of a pencil for the ease of understanding), the elasticity of that rod, the Young's modulus..
2>are there any other factors involved?
 
  • #13
Yaaks said:
ok..
1>Is it possible to measure the vel. @ which the KE travels across AB?,
given,
The RPM for that twist, the circumference of that Pencil (imagining it to be round), the mass-density function (lets take an Iron Rod instead of a pencil for the ease of understanding), the elasticity of that rod, the Young's modulus..
2>are there any other factors involved?

All you need is the density and Young's modulus. From these you can calculate the speed of sound for the rod, and this will be the speed at which the inpulse will travel through the rod.
 

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