# Motion of a very long rod

1. Sep 3, 2011

### Deepak Kapur

Hi all,

A rod 100 km in length is made from a very light material. One end of it is pushed (with whatever energy that may be required for this).

Would the other end move instantaneously or would there be a time lag? If so how much?

Some views (No aggressive ones please, especially from the paid members of this forum).

2. Sep 3, 2011

### bp_psy

The other end will start moving after a period of time equal to the time it takes sound (mechanical waves) to move 100km trough that material.The 'motion' will propagate as a pulse traveling at the speed of sound in that material.

3. Sep 3, 2011

### sambristol

A further view

Newton, Laplace etc and all of classical physics accept the concept of a rigid body so there would be no time delay. A modification of this accounts for the post above by considering the forces between the atoms of the rod and its density, hence the speed of sound in the material is key. The speed is given by the square root of the ratio of youngs modulus and the density. Youngs modulus is a measure of stiffness.

But if you could make a rod with very high youngs modulus and very low density (so the speed of sound would be very high) there is still another limitation thanks to Einstein. In special relativity no information (such that one end of the rod has moved) can be transmitted to another place (ie the other end of the rod) faster than the speed of light approx 3 * 10^8 metres per second.

So the ultimate limit for your 100 Km rod is 10^5/3*10^8 or about a third of a millisecond

4. Sep 3, 2011

### Deepak Kapur

Forgive me for being speculative and digressive. What Sambristol has said has brought another ( you can even say foolish) idea to my mind. Let's say a rod is 1 light year long. A person grows in size so much that he just covers the whole of the rod in one step. Does this mean something at least as far as limit imposed by light is concerned.

5. Sep 3, 2011

### HallsofIvy

Isn't there a FAQ on this? If not, there certainly should be! The "giant person", at least, is new. Deepak, even if you can go one light year with a single step, you still have to make that step. There is a limit to how fast you could move your foot forward.

6. Sep 3, 2011

### Deepak Kapur

I am again being speculative! If such large beings were to exist (even then they will be very, very, very small on the cosmic scale and some kind of comparison can be achieved by thinking of a bacteria and a blue whale, though not correct) will their movements be so slow that it would take 1 year for them to take a single step. Whales don't move slow in comparison to bacteria ( again a far-fetched comparison).

7. Sep 4, 2011

### Naveen123

Such huge beings can't be allowed by nature in order to preserve its laws.

8. Sep 4, 2011

### sambristol

Well if you were that big things would get very strange. If you could step a light year
you would be about 4 light years tall. Given motor nerve signals travel at about 100 metres / second the signal from your brain move your foot would take about 12 million years to make the distance before your foot started to move.

If somehow you could set your (say) right foot off at 99% of the speed of light it would take 99% of a year as seen by the rest of you to complete the step. But it gets stranger. Special relativity tells us that if we observe a clock moving relative to us the clock appears to run slow. So while your, stationary left foot 'thinks' the step takes about a year the moving right foot 'thinks' it takes less time by a factor of sqrt(1-v^2/c^2) or in this case about 51 days.

But dont worry about how your brain would dealt with that because it would not be around to get confused. A body so large would start to collapse under its own gravity. Firstly the atoms of your body would be reduced to a soup of nuclei and electrons similar to the material in a white dwarf star but gravity would continue to squeeze and the electrons would join with the protons in the nuclei to form neutrons – you have become a neutron star.

Gravity still hasn't finished its work, for such a great mass even the resistance of the neutrons would be overcome and the radius would continue to decrease and therefore the surface gravity increase until the velocity required to escape its gravity reaches the speed of light – you have become a black hole.

Not a lot will happen now for a very long time (vastly longer than the current age of the universe) but very quietly you as a black hole have been emitting radiation and hence shrinking very slowly by a process called Hawking radiation. As the hole gets smaller this process increases and increases and the radiation becomes a flood. What happens next? Well nobody really knows or has a good theory because we don't have a workable theory of quantum gravity

Strange what can happen with one step :)

9. Sep 4, 2011

### davenn

so you are inferring there is NO propagation delay of seismic waves through the earth
going by your above reasoning. This is of course incorrect... as there is considerable delay

Dave

10. Sep 4, 2011

### sambristol

Dave,

11. Sep 5, 2011

### Shivam123

hey sambristol;
the concept of how n at what speed force travels in a rigid body has been quite a mystery for me..but what you said about youngs modulus i could not understand please suggest from where should i come to know more about it.And is this true that "motion travels as a pulse at the speed of sound" as bp psy said?

12. Sep 5, 2011

### bp_psy

What I meant was that any element of the rod will start moving when the mechanical pulse generated by the initial push will reach it.That pulse travels at the speed of sound in that material. The speed of sound in a material is determined by its elastic properties and by its density.
You can find out more here:
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html
http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html

Last edited: Sep 5, 2011
13. Sep 5, 2011

### Shivam123

but that "pulse" that we are talking about here is nothing but the force transferred by the neighbouring atoms..isn't it?What i want to know is suppose you hit a rod from front end the particles which received your force travel but those which were connected to the rigid body(say in the rear end) also travel..now this means that the force transferred within the body..and what is the mechanism behind that i want to know and please tell me where or in which book can i find this line-"the pulse travels at the speed of sound"

14. Sep 5, 2011

### CreativeGene

According to the classical theory the body would be considered as rigid, so there will be no delay in the impulse being transmitted to the other end. So in my opinion the body would start to move instantly.

15. Sep 5, 2011

### davenn

I did ... you are inferring zero propagation delay I know from practical experience that there is a delay

show me specifically where you are NOT inferring that

Dave

16. Sep 5, 2011

### jewbinson

I would love somehow to see wave propogation.

I know you can record things in slow motion and there are youtube vids of waves travelling through solids.

But moving a really long light metal rod and seeing the waves of propogation would be 10 times better. But would we be able to notice it?

We would surely need to stand quite far away from the pole because if we were near the pole, the wave would be too fast and we wouldn't see the wave.

So how far away would we need to be to see it? A mile away?

Then we would need binoculours or a very thick pole or both to see the wave.

Is there a practical way to witness it first hand (i.e. without taking a video and then watching it afterwards)?