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chuck22

general speed of light question

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scientists say that it is impossible for objects to move at or faster than the speed of light. so i've got a quick example. let's say i'm holding a rod that is a few miles long, and i have room to rotate it freely. if i rotate it at a quick speed the very end of the rod will be moving faster than the end of the rod that i am holding. infact, if it was a couple of miles long it would be moving very quickly. now let's say that i have a rod that either was long enough or that i could rotate (swing) fast enough that the end of the rod would be moving faster than the speed of light. theoretically, this is possible to make the end of the rod go infinitely faster given you could keep adding length to it or increasing its rotational speed. since objects reach a limited speed, would that be to say that the relationship between the radius and rotational speed of an object also reaches a limit?

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Well given that linear speed and rotational speed are related by the radius of the object, it would make sense that if there's a limit on linear speed, there's also a constraint on radius and rotational speed. However the relationship is v = ωR, so the limit would really be on the product of rotational speed and radius rather than on each variable independently.

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I think the limit would be on the rotational speed. For a particle, the closer you are from the speed of light, the stronger is the force you need to apply if you want it to accelerate. It's like if the mass of the particle was increasing, reaching infinity at the speed of light. Since the lenght of the bar is fixed, the limit would be on the rotational speed.

Now, more interesting : instead of a solid rod, what if you used a laser. if you project a laser on the moon, the spot could move faster than the speed of light. But in this case, no physical object break the speed limit. The photons in the laser ray still travel at the speed of light.

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If you prefer to say that the relationship between the radius and rotational speed of an object has a limit instead of saying that no object can rigidly rotate with angular speed ω and the maximal distance from the rotational axis R when ωR is at least c, sure.

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The reason (or one possible intepretation) why nothing can go faster than light is, that the Mass increases with the speed of the object. If one object would reach the speed if light, it would have infinity Mass, therefor a infinity Force would be neccesary (which does not exit).

You get the same problem in the rotation: If the ends get close to the speed of light, there Mass gets bigger and bigger. You would need a bigger and bigger force to rotate the rod, getting the problem with linear movement.

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ignoring the forces that would make your rigid body not-so-rigid, you could keep applying torque at the centre of rotation, just like you can keep applying force to a particle indefinitely. yet, as its speed comes closer to that of light, its relativistic mass / inertia will approach infinity, and your applied force/torque wont be able to produce an accelaration that pushes it past lightspeed.

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The end of the rod could not go faster than the speed of light becuase of relativity. The rod is a series of particles and as each particle travels faster it need more force to be accelerating by the same amount.

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Well what's funny about the speed of light is that there is no such thing as speed at that speed. Before you flame me on this,I have a degree in physics and think about this. Scientist have proven that the faster you go the slower time is. So, that when you go the speed of light there is no time. That's right boys and girls at the speed of light there is no time. With no time the term speed doesn't make sense.

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chuck22: The answer to you question is this:
there's no such thing as a completly rigid body. if you move one end of a rod then the other end will start moving only after the amount of time that it takes sound (the sped of sound is the speed that vibrations are propagated thru the body) to move thru the rod. so when you start spinning one end of the rod the other end will only start spinning in L/Vs time were L is the length and Vs is the speed of sound in the rod. because of this the rod will get all twisted up and no part of it will move faster than light.

egwenejs: when we say that "at the speed of light there's no time" that means that in the lights frame no time passes. but obviously in our frame it takes light a finate time to go between two points. so in our frame there is such thing as speed at light speed and theoreticlly speed has meaning even at more than light speed. but in the frame of the body theoreticlly going faster thaan the speed of light time would be going backwards! that's one of the reasons that nothing can go faster than light, because if there were than it would destroy causulty!

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If an object goes faster than the speed of light it goes back in time, right? There is always stuff moving around the object, seen from the object p.o.v. As long stuff is moving relative to another there is no issue. In the end all is relative and there is no 'absolute'. I don't see a limit anywhere.

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