# Rotate a long bar in space and get close to (or even beyond) the speed of light $c$

Imagine a bar

spinning like a helicopter propeller,

At $\omega$ rad/s because the extremes of the bar goes at speed

$$V = \omega * r$$

then we can reach near $c$ (speed of light) applying some finite amount of energy just doing

$$\omega = V / r$$

The bar should be long, low density, strong to minimize the amount of energy needed

For example a $2000\,\mathrm{m}$ bar

$$\omega = 300 000 \frac{\mathrm{rad}}{\mathrm{s}} = 2864789\,\mathrm{rpm}$$

(a dental drill can commonly rotate at $400000\,\mathrm{rpm}$)

$V$ (with dental drill) = 14% of speed of light.

Then I say this experiment can be really made and bar extremes could approach $c$.

What do you say?

EDIT:

Our planet is orbiting at sun and it's orbiting milky way, and who knows what else, then any Earth point have a speed of 500 km/s or more agains CMB.

I wonder if we are orbiting something at that speed then there would be detectable relativist effect in different direction of measurements, simply extending a long bar or any directional mass in different galactic directions we should measure mass change due to relativity, simply because $V = \omega * r$

What do you think?

• V(with dental drill) = 14% of speed of light :-o You scared me with this. I actually had to calculate it to understand what you meant. =P Jan 14 '11 at 0:29
• haha now that you said it, I see it's a funny statement
– Hernan Eche
Jan 14 '11 at 12:08
• "... simply extending a long bar or any directional mass in different galactic directions we should measure mass change due to relativity". Well Michelson-Morley thought of something similar. The answer is no. We won't detect change in weight or size. By principle of relativity. Because we travel with the same speeds as the bar. Apr 28 '11 at 21:02

Imagine a rock on a rope. As you rotate the rope faster and faster, you need to pull stronger and stronger to provide centripetal force that keeps the stone on the orbit. The increasing tension in the rope would eventually break the it. The very same thing would happen with bar (just replace the rock with the bar's center of mass). And naturally, all of this would happen at speeds far below the speed of light.

Even if you imagined that there exists a material that could sustain the tension at relativistic speeds you'd need to take into account that signal can't travel faster than at the speed of light. This means that the bar can't be rigid. It would bend and the far end would trail around. So it's hard to even talk about rotation at these speeds. One thing that is certain is that strange things would happen. But to describe this fully you'd need a relativistic model of solid matter.

People often propose arguments similar to yours to show Special Relativity fails. In reality what fails is our intuition about materials, which is completely classical.

• I didn't understand, you say the bar will break? or that think about the bar will break is our intuition about materials? I want to know what will happend and what is the physic restriction of doing the experiment (of course I suposse something must be wrong, but I asked to know it deeper) thanks
– Hernan Eche
Jan 13 '11 at 15:06
• @Hernan: both. The bar is not rigid. It will first bend because the signal has to travel from one end to the other; the end closer to you is already moving but the far end won't start moving until the stress wave reaches it. Also, there will be huge stress on the material in the radial direction which will eventually break it. Jan 13 '11 at 17:01
• so perhaps relativity limit the posible size of things.. because if something have too much lenght it divides at first rotation because some points behave massy and breaks
– Hernan Eche
Jan 13 '11 at 20:00
• @Hernan: actually, relativity limits the angular velocity you can get an object up to. Jan 13 '11 at 22:26
• @Hernan: but remember that you'd need lot of energy to rotate that object in the first place! E.g. you'd need an infinite amount of energy to accelerate a particle to the speed of light. And that's just a particle, not a huge extended object. Second point is that in nature there are no solid objects on macroscopic scales. On the scales of galaxies there is just intergalactic dust and stars following the rules of General Relativity. Jan 13 '11 at 22:33

There is a real object with relativistic speed of surface - millisecond pulsar. The swiftest spinning pulsar currently known, spinning 716 times a second. Surface speed of such pulsar with radius 16 km is about $7*10^7$ m/s or 24% speed of light.

It is calculated that pulsars would break apart if they spun at a rate of more than 1500 rotations per second.

• great to know !
– Hernan Eche
Jan 13 '11 at 20:03

In your calculations you assume that your propeller is a rigid body.

You cannot use that assumption, when your speeds are not much smaller than the speed of light. Because "there are no rigid bodies in relativity".

• MMmm this let me thinking..So..that could lead a definition of body, i.e. body can only exist in one and only one inertial frame of reference, never in two at same time
– Hernan Eche
Jan 13 '11 at 19:56

remember that in a three-dimensional description of special relativity the impulse of an object is given by

$$\mathbf{p} = \gamma m \mathbf{v}$$ with the so-called Lorentz-factor $$\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$$

Now, do you think you can accelerate the masses within the slab to a speed greater than light or do you think that something is wrong with your physical model of the system?
Sincerely

Robert

• Nice letter, I want to know what is wrong in doing the real experiment, or thinking you can deliver energy (taking your time) and accelerate the bar (gradually) to transform that energy and angular velocity in a higher tangential velocity, angular momentum conservation will store the energy so I can continue adding more and more energy
– Hernan Eche
Jan 13 '11 at 15:02
• Hernan writes "near c" but he did not write about "speed greater than c". Apr 28 '11 at 21:03
• @Andrei: It remains the same argumentation. Greets Apr 29 '11 at 7:05

I say no. Assuming all the practicalities work, you can get arbitrarily close to c. But not reach c. You can see this easily from the relativstic formula for kinetic energy:

$E_k = mc^2(\frac{1}{\sqrt{1-v^2/c^2}}-1)$

As $v$ approaches $c$, the energy you need to supply to a particle at the end of the bar tends to infinity.

• The energy needed would vary in every segment of the bar because its speed would be different, so the bar would break only by relativity effects ? perhaps
– Hernan Eche
Jan 13 '11 at 15:14
• bar would break because it" reacts" on force with the speed of sound in it, which is not more than 3000 m/s. When you cross 3000 m/s bar is like a liquid :-) Jan 13 '11 at 15:47
• Your assumption of "all the practicalities working" is far too big of an assumption; you're assuming away the very heart of the question, which is: can I do this using a rigid body. Dec 18 '11 at 3:41

Dear Hernan, as the distant parts of the bar are approaching the speed of light, they become heavier, so it becomes harder to accelerate them: you can never reach (or surpass) the speed of light. It doesn't matter whether you try to accelerate the "final segments" of the bar by jets or by their attachment to the rest of the bar that is being pushed in the middle: the speed of light can never be reached.

If you want to speak in terms of torques and moments of inertia (of the bar), the moment of inertia goes to infinity - much like the mass itself - when the velocity of some points on the bar approaches the speed of light. So much like you have to modify the formulae for masses of moving objects by relativistic effects, you need to modify the formulae for the moments of inertia.

So your statement that you need a finite energy to get to the speed of light is invalid. You would need an infinite energy. For speeds below the speed of light, the total energy that you need can simply be calculated as the sum of the kinetic energies of all the segments of the bar.