Rotate Pencil About Axis AB: What Obs. C Sees

[Yaaks]

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

A ---------------------------------------------B
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|
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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'.)

 

[Yaaks]

C is the mid-point of AB, Plz ignore the typing error...
Thanx

 

[DrGreg]

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.

 

[Yaaks]

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...

 

[DrGreg]

Whether it breaks or not depends how much force you apply and how quickly.

 

[Yaaks]

....Assuming tht the force generated @ A travels along AB @ the speed of light?

 

[jtbell]

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.

 

[Chronos]

The pencil will break. Mechanical waves travel much slower than 'c'. Major league baseball players can break bats merely by swinging them.

 

[JesseM]

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.

 

[Yaaks]

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...

 

[Janus]

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)

 

[Yaaks]

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?

 

[Janus]

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.