Spinning faster than c?

[dirtyamerica]

This has been a thought in my mind for several years now and I remembered it while lurking here and thought I'd ask you all as some of you will surely give me some great insight.

 

I'm aware that faster-than-light speed isn't possible because of the mass issue among other things. But we tend to think of objects traveling in a single direction, trying to reach "c". So here's another approach..

 

So here's my question. In theory, could you build a very big wheel with a circumference of 186,000 miles or so and apply an energy source close to its axle that could spin it at 1 revolution per second or slightly faster, thereby causing some points on its outer edge to travel at (or faster than) the speed of light. There is a mechanical advantage here much like a bicycle tire on a geared bike.

 

What factors would make this impossible? I'm sure the driving energy and durability of the wheel are issues. Would centrifugal force tear the wheel apart before you reached desired speed? etc.

 

I'm pretty rusty at this stuff and I can prove that "cognitive decline" does happen when you work rotating shiftwork so please go easy on me. Thanks!

[swansont]

The material would structurally fail long before c was reached. One of the implications of relativity is that rigidity of material is finite.

[timo]

I think another issue would be the energy required to get the wheel spinning so fast. You should ultimatively run into the "no matter how much energy I put in, the velocity will always be <c" problem.

[Severian]

This would actually make a nice tutorial problem. If you properly take into account length contraction, you will see that you can never make a point on the rim of the wheel go faster than c.

[Meir Achuz]

In theory, could you build a very big wheel with a circumference of 186,000 miles or so and apply an energy source close to its axle that could spin it at 1 revolution per second or slightly faster, thereby causing some points on its outer edge to travel at (or faster than) the speed of light. Thanks!

A spinning wheel cannot be treated in SR.

In principle, it should be treatable in GR, but I don't know of anything definitive in the past 80 years.

[Connor]

well, even if the inner parts aren't travelling near c the outer parts are and it would take infinite energy to accelerate

 

Also, as swansont said no material is 100% rigid, in fact, information can only travel at c so maybe the inner part would rotate faster than the inner part

[Daecon]

This would actually make a nice tutorial problem. If you properly take into account length contraction, you will see that you can never make a point on the rim of the wheel go faster than c.

Do you have any more information how length contraction would apply to a wheel spinning at speeds approaching c?

 

Would it not violate the πr² rule?

[swansont]

Do you have any more information how length contraction would apply to a wheel spinning at speeds approaching c?

 

Would it not violate the ?r² rule?

 

^{[math]\pi r^2[/math]} applies in Euclidian space, which this is not.

[JustStuit]

The problem would be the Fc needed to keep it in circlular motion would be astronomical.

[EvoN1020v]

Objects can't reach past the speed of light, because 1: resistance of air. 2: not enough energy.

 

Plus, using the image of a space shuttle, as it fl really fast, it gradually would go out of the Earth's atmosphere, so it will experience different types of force in the space. I mean, 1.30 x 10^11 miles per second? That's incredibly fast.

[5614]

I like this question and I asked it here on the forums a while back, here's the thread:

 

Oh, it isn't quite the same thing which I asked. My idea was having a spinning disc on a spinning disc etc. The idea of the outside of a disc spinning faster than the inside did crop up in post #7 though, here's the link:

 

http://www.scienceforums.net/forums/showthread.php?t=9584

[timo]

Now you got me curious: Why isn´t this a flat minkowsky metric?

 

For me, the problem looks quite simple:

I start with a wheel which has a mass distribution [math] \rho = \frac{M}{2\pi} \delta(R-r) [/math]. Then I start rotating it with an angular velocity [math] \dot \phi [/math]. For all points on the circle, the velocity will be perpendicular to the radius, therefore I wouldn´t expect any length contraction. After integrating over the whole space, the total kinetic energy of the rotating ring will then be [math] E(\dot \phi) = (\gamma-1) M = \frac{M}{\sqrt{1- (R \dot \phi)^2}} - M [/math] which of course diverges for [math] \dot \phi \to 1/R = c/R [/math] which is equivalent to a rotation frequency of [math]f \to \frac{c}{2\pi R} [/math].

Or in other words: As the frequency approaches that at which the particles in the ring had speed of light, the energy diverges. For any finite energy the system has, the particles will move slower than lightspeed.

[Severian]

For all points on the circle, the velocity will be perpendicular to the radius, therefore I wouldn´t expect any length contraction.

 

I don't understand what you mean by this sentence. The edge of the rim is moving with respect to the stationary observer at the centre, so it will be length contracted. An infinitesimal length dx on the rim in the wheel's rest frame will become [math]\frac{1}{\gamma} dx[/math] in the observer's frame. It doesn't make any difference whether the velocity is perpendicular to the radius.

[ydoaPs]

atheist, the radius wouldn't contract, but the circumference would

[timo]

What I meant is that the value R is unaffected by the rotation. Possibly a superfluous statement, but it didn´t seem obvious to me, at least.

 

EDIT2: k, I understand why you were talking about length contraction, now. I was actually going over rest-mass which is an invariant (my density rho would have been a "rest-mass density" not a zero-component of a momentum tensor and therefore invariant under moving <-> nonmoving) and then got it moving.

[whap2005]

The material would structurally fail long before c was reached. One of the implications of relativity is that rigidity of material is finite.

I'm not sure this is entirely correct. If you could somehow place a mass at the center of this device and increase the density of the of the object so that its gravity would increase with the rate of spin, it could have the effect of keeping the device from flying apart. My only advice is to make sure you have the device insured since you may end up with a black hole before you actaully reach C...

[JustStuit]

You would have to make it out of something very very rigid and strong.

[whap2005]

You would have to make it out of something very very rigid and strong.

 

Damn..there goes my styrofoam and toilet paper theory..

 

Actually if you’re using gravity to keep it all together, strength isn't as important as mass. Your going to want to keep this device as 'light' as possible. Less mass means less energy needed to accelerate the object.

[JustStuit]

You need a [math] F_c [/math] which is a force towards the center of the circle. In this case it is either [math] F_n [/math] if it is horizontal or [math] F_n [/math] and [math] F_g [/math] if vertcal. The [math] F_n [/math] relys on the soundness of the material so it must be unreasonably (and impossiblely) rigid.

[whap2005]

You need a [math] F_c [/math] which is a force towards the center of the circle. In this case it is either [math] F_n [/math] if it is horizontal or [math] F_n [/math] and [math] F_g [/math] if vertcal. The [math] F_n [/math'] relys on the soundness of the material so it must be unreasonably (and impossiblely) rigid.

 

I don’t think you’re including gravity in your math. Without a force to counteract centripetal force, you would then need a device that is impossibly strong. If you use gravity to counter centripetal force, then why would it matter how rigid it is?

[zebov]

ok, how about two 186000 mile diameter merry-go-rounds both spinning clockwise and sped up using the same technique as discussed above as fast as they will go (>.5c). I ride one on the outside, you ride the other on the outside, what do we see when we pass each other? How fast would we be going relative to each other as we passed?

[qwerty]

If we are travelling through space at speed x m/s....... wouldn't the wheel need to spin at 300,000 km/s - x m/s...... ?

 

Also if this wheel is travelling at 250,000 km/s ... wouldn't a tiny amount of force cause it to increase in speed (i am talking about the points on the circumference).... which means that every tiny amount of force we spin the wheel wiht will always increase the speed, no matter how small the force is. there is no force acting against it.

[clarisse]

^{[math]\pi r^2[/math][/sup'] applies in Euclidian space, which this is not.}

 

^{What kind of space is this in?}

[swansont]

I'm not sure this is entirely correct. If you could somehow place a mass at the center of this device and increase the density of the of the object so that its gravity would increase with the rate of spin, it could have the effect of keeping the device from flying apart. My only advice is to make sure you have the device insured since you may end up with a black hole before you actaully reach C...

 

Limited rigidity is perhaps more easily seen with a long rod; if you push on one end, the other end does not move instantly.

[swansont]

What kind of space is this in?

 

Curved. It was this, or a similar, thought experiment that's in Einstein's papers that led him to conclude that accelerating frames of reference are curved spaces, and that led to general relativity.