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PaulRacer
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If there was a stick the length of the diameter of Earth spinning in space for the same amount of time at the same rate as earth, would it appear as a spiral?
From a top-down view of our solar system, the path traced-out by the stick would look like a spring laid on its side and crushed.PaulRacer said:If there was a stick the length of the diameter of Earth spinning in space for the same amount of time at the same rate as earth, would it appear as a spiral?
There is no such thing as "accumulated inertia", there is only inertia. Perhaps you are thinking of momentum, which is inertia times speed (in rotation, moment of inertia times rate of rotation). Or for energy, rotational kinetic energy.Is it possible that there is any stored energy in this "twist" from the accumulated inertia?
russ_watters said:After there is no more torque applied and the vibrations have been dissipated by damping, why can't the rod be perfectly straight?
russ_watters said:From a top-down view of our solar system, the path traced-out by the stick would look like a spring laid on its side and crushed. There is no such thing as "accumulated inertia", there is only inertia. Perhaps you are thinking of momentum, which is inertia times speed (in rotation, moment of inertia times rate of rotation). Or for energy, rotational kinetic energy.
...This doesn't appear to me to have anything to do with Relativity.
That question was for Frederick - I don't see why he thinks there is a twist.PaulRacer said:Is this a rhetorical question? I know very little about physics but I am trying to understand relativity. All I have is speculation if it's not a rhetorical question.
I'm an engineer, but in any case, Newton's first law applies. There is no accumulation of or dissipation of energy in a constantly moving object.PaulRacer said:Sorry, I was trying to build to something without using only my assumptions. I appologize for the terminology. I meant the possible accumulation of energy through the spinning of an object for a long period of time and how this relates to angular velocities and related spacetime implications. It just seemed possible to me that if the spacetime in the center of a rotating object was different than the ends then there would be a lag between the matter at the ends and the matter at the center resulting in a spacetime "tug". I have no idea so I thought I would ask physicists like you.
The rod will be heated a bit when we apply the torque to the center, but we'll wait long enough for the rod to cool down again.PaulRacer said:I meant the possible accumulation of energy through the spinning of an object for a long period of time and how this relates to angular velocities and related spacetime implications.
The problem is hard enough in Minkowski space. I'd rather not worry about spacetime curvature and that sort of thing.PaulRacer said:It just seemed possible to me that if the spacetime in the center of a rotating object was different than the ends then there would be a lag between the matter at the ends and the matter at the center resulting in a spacetime "tug".
Actually, what I had in mind when I wrote #8 is that we apply a torque for a while and then let it go. It seems to me that the rod will still end up being twisted, after all the vibrations have died down (for the reasons I tried to explain in #14, where I did talk about repeating the procedure forever, or at least long enough for some of the relevant speeds to get close to c).DrGreg said:Fredrik, I think Russ was confused because earlier, I think, this thread was talking of applying a torque to set the rod in motion and then releasing the torque to let it continue spinning. Whereas you are talking about applying a continuous torque forever.
Fredrik said:Actually, what I had in mind when I wrote #8 is that we apply a torque for a while and then let it go. It seems to me that the rod will still end up being twisted, after all the vibrations have died down (for the reasons I tried to explain in #14, where I did talk about repeating the procedure forever, or at least long enough for some of the relevant speeds to get close to c).
If you have the rod spinning very fast and you apply more torque to the center, it will accelerate more and twist while it is accelerating. Then when you release the torque it will stop accelerating and straighten out. This has nothing whatsoever to do with Relativity. It doesn't matter how fast or slow the rod is rotating, it will always be true.Fredrik said:a) One is that the rod stays straight. In this case, the length of the rod sets an upper bound for the angular velocity. (The speed of the edges must be <c). The problem I have with this option is that when the rod is close to its upper bound angular velocity, we should still be able to apply more torque to the center to get the center parts to move faster, and now the rod has to bend and stay bent (or broken) after all the vibrations have died down. Nothing in relativity behaves this way. Light speed isn't a "barrier" that we suddenly "hit". All the effects that are large near the speed of light are present at small velocities too.
I don't understand what you're saying here. When a rod bends, the end will be at a shorter distance from the center than when it is straight, which changes the angular momentum. Is that what you're getting at? Again, this has nothing to do with relativity: When the torque is released and the rod straightens, angular momentum will be conserved and the rod will be spinning at whatever rate conservation of momentum requires.b) The other possibility is that the edges lag behind the parts near the center even at low angular velocities and, as the internal forces try to restore the length of each atomic-scale segment, the edges get pulled closer to the center, ensuring that they won't move faster than c, no matter how fast the parts at the center are moving. In this case, the distance between the edges and the center goes to zero as the speed of the parts near the center goes to c, so the rod wraps itself around the center point. A real rod would of course break long before that happens.
No, it isn't hard. If there is no torque, there is no force perpendicular to the rod, so the rod must be straight. Centrifugal force will stretch the rod a little, but that effect probably isn't that tough to calcluate.I guess b) is a partial answer to the question I asked yesterday. When we apply torque to the part near the center, the rod is stretched, and whatever shape it finally settles down to will be the result of internal forces trying to restore the distance between nearby atoms to what it was before...plus a correction due to the centrifugal force. It looks like it would be hard to actually calculate the shape of the rod.
Yes.Fredrik said:Hm, OK I think I get it. If we take a (straight) rod that's already spinning so fast that the edges are moving at 0.99c, and we apply more torque for a while to get the center spinning faster and then wait until the vibrations have died down, the edges will be moving at (say) 0.999c, the center will have slowed down to the same angular velocity as the (new) angular velocity of the edges, and the rod is straight again.
Yes, that sounds reasonable. The key there is while you aren't accelerating the midpoint of the rod anymore, you are accelerating the edge and so you are applying a torque and bending the rod. From the point of view of a person near the center of the rod, the outer edge wouldn't seem to be accelerating much, but in terms of the increase in momentum, it could still be accelerating quite a bit.Suppose that we now apply more torque to get the center (say the first meter) to rotate at a 1% greater angular velocity, and then force the center to rotate with that angular velocity forever. (Note that the acceleration period is rather short, but then the center is held at a fixed angular velocity forever...and yes, this is a different scenario than the one I've been considering until now). In this case the rod can't straighten out. If it could, the edges would be moving faster than c. It also can't settle down to one specific shape. If it did, then it would have a constant angular momentum. But it can't have a constant angular momentum, because we're constantly applying a torque. To see why we must be applying a torque, just think about the fact that if we let the rod go, the center would slow down as the rod straightens out. So by keeping the center at a fixed angular velocity, we're doing work against the internal forces that are trying to straighten out the rod.
Since the rod can never settle for one specific shape, it must continue to get more and more deformed until it breaks.
Now, instead of applying a constant torque, you're applying whatever variable torque is necessary for the centre to maintain a constant angular velocity [itex]\omega[/itex]. Well, at first, yes, the rod will continue to deform (assuming it doesn't break). But as it deforms, the maximum radius of the whole deformed structure will shrink. If the radius ever shrunk below [itex]c/\omega[/itex], there would no longer be any relativistic objection to the tips moving with angular velocity [itex]\omega[/itex], and then zero torque would be required to maintain the motion. But without a torque the rod would straighten out again. So I guess what happens is the radius tends to [itex]c/\omega[/itex] as [itex]t \rightarrow \infty[/itex]. Does that sound plausible?Fredrik said:Since the rod can never settle for one specific shape, it must continue to get more and more deformed until it breaks.
What do you mean? It sounds like you answered the question in the question. ("If I go to New York, what city will I be in?" ) Only a black hole would remain. Besides, if the rod is massive enough to form a black hole, I think that would happen long before we can get it spinning that fast.PaulRacer said:What would happen after all of this spinning if the stick rapidly shortened itself to singularity like a black hole does?
I don't see a way to derive the results we're talking about from time dilation alone, and the last part of that sentence is wrong (if I have understood what you're saying).PaulRacer said:The speed of light is obviously a brake of sorts but only because time slows at such a rate at high velocities that the speed of light at the edges relative to the center is multiplied.
You shouldn't say things like that. You can talk about what happens to other variables in the limit v→c, but there's no such thing as "at the speed of light". Massive particle's can't even move that fast. Massless particles can (they can't move at any other speed), but there's no natural way to associate an inertial frame with their motion. See my posts in this thread for more on that.PaulRacer said:This is due to the fact that (if I understand it correctly) time would theoretically stop at the speed of light.
c doesn't go to infinity in the limit v→c.PaulRacer said:Therefore the speed of light would become infinite if you could travel at c because speed is measured in units per hr./min./sec.
I don't really follow your reasoning, but you seem to be confusing GR stuff with SR stuff. There is no gravity in SR, and therefore no curvature, but the rod still gets twisted due to the finite propagation speed of the deformation we're doing to the center. This doesn't really have anything to do with relativity. To see a truly relativistic effect, we must do something special. We can e.g. keep applying torque to the center to keep it rotating at an angular velocity that's too fast for the edges to keep up. (See my last post before this one). There's nothing in pre-relativistic physics that would prevent this rod from straightening itself out, but SR says that the rod will continue to get more and more deformed.PaulRacer said:If this is the case, the rod wouldn't need torque to deform, only to be spinning for a long period of time because of warped spacetime due to angular velocities. Once the spacetime is warped and the rod is twisted like a spiral, how could it possibly straighten if time was equalized throughout the rod by stopping the spin? If you stopped the spinning, more time would have still passed relatively in the center due to slowed time at the higher velocities near the ends. Seems to me that the only way to straighten it is a counter rotation for the identical amount of time at the identical velocity. If this sounds somewhat reasonable I have more questions. If not, I guess I have many more questions.
The "Earth's Diameter Stick" is a scientific instrument used to measure the diameter of the Earth. It is essentially a spinning spiral with a known length and rate of rotation, which allows scientists to calculate the Earth's diameter.
The "Earth's Diameter Stick" is a very accurate instrument, with a margin of error of only a few kilometers. This level of precision is achieved through careful calibration and the use of advanced technology.
The "Earth's Diameter Stick" has many practical applications in the field of geodesy and geophysics. It can be used to accurately map the Earth's surface, measure changes in the Earth's shape and size, and aid in navigation and cartography.
The "Earth's Diameter Stick" works by spinning at a constant rate and measuring the time it takes for one full rotation. This information, along with the known length of the stick, can be used to calculate the Earth's diameter using mathematical formulas.
No, the "Earth's Diameter Stick" is not the only method for measuring the Earth's diameter. Other techniques, such as satellite imagery and laser ranging, are also used by scientists to accurately measure the Earth's size and shape.