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Quote from: Malamute Lover on 02/08/2020 04:18:03Quote from: Kryptid on 01/08/2020 00:42:19Quote from: Malamute Lover on 31/07/2020 23:54:22Lorentz contraction is relative, not real.What about it being relative makes it not real?How about different observers seeing different things? Who is right?What do you mean by real?In the example @Kryptid gives further down a traveller can be seen by earth observers to take (say) 4yrs to travel to a distant star - based on the distance they measure. The traveller, however, sees the distance to the star length-contracted and so takes less time to travel that distance. The experience is real for both of them. (Time dilation and length contraction are effectively the same thing).If you think these effects are not real you will have to rewrite what we understand about electricity and magnetism and also a great deal of chemistry. Good luck with that
Quote from: Kryptid on 01/08/2020 00:42:19Quote from: Malamute Lover on 31/07/2020 23:54:22Lorentz contraction is relative, not real.What about it being relative makes it not real?How about different observers seeing different things? Who is right?
Quote from: Malamute Lover on 31/07/2020 23:54:22Lorentz contraction is relative, not real.What about it being relative makes it not real?
Lorentz contraction is relative, not real.
The gaps between blocks are said to appear because the radius of the circle is taken to be constant.
It is my contention that the spokes will maintain their length but will curve due to differing time dilation along the length. The fixed length of the spokes but bent into a curve will result in a reduced radius and the rim holding the blocks will contract as expected. No gaps will appear.
First some comments about time dilation. The pilot of a rocket ship that has accelerated to 0.99 c will experience a time dilation factor of about 7. The clock on the ship will be running 7 times slower than before the acceleration.
That is, watching landmarks go by, he sees himself as traveling at almost 7 c.
(Either that or he thinks the distances have shrunk.) But after several years of sightseeing, he decelerates and gets back home again, and finds that his twin brother has aged much more than him. He realizes that acceleration really did slow his clock and that he was not traveling as fast as he thought. He was really traveling much slower.
Unlike time dilation due to different relative inertial speeds, time dilation resulting from acceleration is real and has real consequences. This is the resolution of the so-called Twin Paradox.
In the case of the spinning wheel, different portions of each spoke are traveling at different speeds. The time dilation factor increases as one travels up the spoke from the center.
A clock carried up from the axle to a certain point and back down again will have recorded less time than a clock that stayed at the center. The further up the clock is taken, the greater the discrepancy when brought back.
When the wheel was spun up, the different parts experienced different accelerations, and/or different centripetal accelerations as the wheel turns.
This is acceleration-based time dilation and it is therefore real. At each level, the clock is slower than at the center and the real speed is less than an observer at that level thinks it is.
Since the angular displacement would vary at each level, the spoke would curve.
...Nope. The ship must accelerate into order to reach such a very high velocity. That is an acceleration that is not experienced by the observer on Earth. So the situation is not symmetrical.
Quote from: Malamute Lover on 01/08/2020 16:53:41The gaps between blocks are said to appear because the radius of the circle is taken to be constant.There are actually three distinct scenarios.1) You have a solid ring that spins. It contracts as you spin it. A shrinking ring (that reduces in radius from any perspective) seems awful real to me. Using this scenario, I can pass one wedding ring through another identical one by spinning it. That's real contraction, or it couldn't be done. It isn't observer dependent.You are sort of describing such a thing below, except with superfluous spoke that will bend because they're too long, so they serve no purpose other than to be deformed by being squashed.
2) Spoke scenario, or the roller coaster track, which is essentially the same scenario. Here the radius is held constant by the non-contracting straight spoke, or by the stationary track. There is no solid ring, but a series of detached adjacent blocks. If there are spoke, you have essentially a row of independent pendulums. If a track, you have a row of 'bumper cars'. Spin it up and gaps form between the blocks, and more can be inserted if you like.Observers in any frame will agree on this, but you seemingly are in denial of it.
3) The actual Ehrenfest scenario where he takes a non-Euclidean 3 dimensional solid (a spinning cylinder) and declares it paradoxical when its non-Euclidean properties are illustrated. If the object is rigid, it shatters as soon as you attempt to change its angular speed. That shattering is an objective effect that any observer in any frame will witness. There are other ways to create non-Euclidean objects. Find a neutron star and build a sort of feeding trough that encircles it at some low altitude, say 10 km wide and thick. Fill that trough will some material that hardens into some rigid object, and remove the trough. In normal space, the outside radius will be 60π km greater than the inside radius, but with this object the difference will be less than that, depending on how close to the star you build it. Remove the object from the vicinity of the neutron star and it shatters just like the Ehrenfest object. Ehrenfest found a way to create such an object in flat spacetime using length contraction, but it doesn't work if length contraction isn't real.
QuoteIt is my contention that the spokes will maintain their length but will curve due to differing time dilation along the length. The fixed length of the spokes but bent into a curve will result in a reduced radius and the rim holding the blocks will contract as expected. No gaps will appear.If you content that the curving spokes is what draws the blocks in, that wouldn't work if the blocks didn't actually contract since they would not fit in the smaller radius. If the radius of a spinning wheel does contract, that is a real effect visible to any observer, so not a relative effect.This assertion that it is the spokes bending and curving, pulling in the separate blocks is contrary to all accepted physics. It is a fantasy assertion that you cannot support. It seems you are one of those that will hold to your assertions forever rather than show a willingness to learn.
QuoteFirst some comments about time dilation. The pilot of a rocket ship that has accelerated to 0.99 c will experience a time dilation factor of about 7. The clock on the ship will be running 7 times slower than before the acceleration.No frame reference, so that statement is ambiguous. It will be running 7 times slower relative to the frame in which the ship is moving at .99c. Not saying you're wrong, just sloppy. It's running at normal rate relative to the ship of course.
QuoteThat is, watching landmarks go by, he sees himself as traveling at almost 7 c.If there is a grid with mileposts he can watch, then yes. You can call that his proper velocity if you want, which is what you get by simply multiplying his proper acceleration by his proper time under that acceleration. There's no limit to proper velocity since it accumulates additively, not relativistically.
Quote(Either that or he thinks the distances have shrunk.) But after several years of sightseeing, he decelerates and gets back home again, and finds that his twin brother has aged much more than him. He realizes that acceleration really did slow his clock and that he was not traveling as fast as he thought. He was really traveling much slower.What an absolute way of putting it, but yes, in the brother's frame, he was travelling at nearly c. In his own frame, he wasn't moving at all, only the length-contracted markers were. He knows very well that those moving markers do not mark distances properly and can not move faster than light, as evidenced by the fact that he can see the one's coming at him. If they were moving at nearly 7c, they'd not be visible at all until they had passed, just like you can't hear a supersonic jet coming at you. So he knows those markers are moving at about .99c and are nowhere near a km apart. To assert otherwise is to assert light moving faster than c, something I'm starting to see a lot of here.
QuoteUnlike time dilation due to different relative inertial speeds, time dilation resulting from acceleration is real and has real consequences. This is the resolution of the so-called Twin Paradox.So I have four observers Alice, Bob, Charlie and Denise. Alice was always on Earth. Charlie came to Earth with Denise and Charlie accelerated to Earth frame to marry Alice. Bob accelearted to match speeds with Denise to marry her. Denise and Alice have thus never accelerated, and the other two have.So according to your statement above, time dilation of the clock on Earth is real according to Charlie because he accelerated to Earth frame, but it is not real for either Alice or Denise, neither of whom have ever accelerated. Meanwhile dilation of the clock on the ship with Bob and Denise is real to Bob (having accelerated to that frame), but not to Denise right there with him.Sounds very inconsistent that the same clock is really dilated and also not.
Also, length contraction in all 3 scenarios at the top of this post is very real by your definition since there is a very real consequence (observed by anybody) in all three situation.
QuoteIn the case of the spinning wheel, different portions of each spoke are traveling at different speeds. The time dilation factor increases as one travels up the spoke from the center.Agree. Any clock nearer the center will run objectively faster than one further out. ISS clocks run faster than sea-level clocks for this reason, but GR must be invoked to compute exactly how much.
QuoteA clock carried up from the axle to a certain point and back down again will have recorded less time than a clock that stayed at the center. The further up the clock is taken, the greater the discrepancy when brought back.Also how long it spent out there. You'd have to integrate the curve.If this is not a reasoning why length contraction doesn't actually occur, then you're getting way off topic.
QuoteWhen the wheel was spun up, the different parts experienced different accelerations, and/or different centripetal accelerations as the wheel turns.In scenario 3, and also the spoked wheel in post 2, nothing was spun up. There was never any acceleration. In scenario's 1 & 2, there is angular acceleration involved.
QuoteThis is acceleration-based time dilation and it is therefore real. At each level, the clock is slower than at the center and the real speed is less than an observer at that level thinks it is.Oh, so if I build a clock on the rim of an already-spinning wheel, it will stay in sync with the clock at the axle? If not, what do you mean by this distinction between acceleration-based real time dilation and not-real?Suppose Bob passes Earth at .866c without acceleration, syncing his clock to Earth when he's in its presence. Both say zero. After a year, he smashes the clock works, freezing it at its reading of 1 year. He turns around, builds a new clock, sets it to zero and smashes the workings again, freezing it at 1 year as well. He then decelerates. Now he has two clocks that have never accelerated (at least not while working) that cumulatively account for 2 years, but 4 years have gone by on Earth.
I'm sorry, but your stories are getting sillier and sillier, seemingly in a desperate attempt to not admit you've made a mistake. Einstein never mentioned any distinction between real and fake time dilation, or real and fake length contraction. Measurements using light would be different than empirically measured if length contraction wasn't real. All you have to do is time light as it goes from one end to the other and back in a moving train. Measure the time with stationary synced clocks (OK, you have tried to counter this by flat out denial of the possibility of syncing stationary clocks). It will take way too long if the train is not really contracted. A history of acceleration of the train plays no role in the equations involved.
QuoteSince the angular displacement would vary at each level, the spoke would curve.Time dilation has no effect on the curvature of the spokes. They're effectively strings. Time dilation does have an effect on the angular velocity of the wheel. An observer at the axle would measure a smaller angular velocity than one at the rim, which is why for relativistic wheels, we specify linear rim speed, not radians per second. The spokes are straight unless there is angular stress on them such as the wheel being accelerated by torque being applied at the hub, but no such torque exists in our examples. All measurement are done in steady state. Yes, if I put enough change in the rate of torque on a real bicycle wheel, the change would need to propagate up the spokes to the rim at the speed of sound, causing a momentary wave to travel up the spoke. That would bend it a bit just like a sideways yank on a garden hose causes a bend to travel up the hose. A freely spinning wheel has straight spokes so long as there is any tension on them.
... Are you denying time dilation?...Contraction is relative, not objective....
...Time dilation can be seen to be real when a clock that has undergone acceleration and brought back into a common inertial frame with a clock that has not accelerated. Try restating your scenario with some common inertial frame clock comparisons. ...
The example presented by Kryptid is in question, therefore your argument based on Kryptid's comment is in question as well,
What is real is what is going on in 4D Minkowski spacetime. We time bound observers only get to see a slice at a time depending on our reference frames.
Multiple observers in different reference frames see different things. None of them see the real thing. Relativistic effects are relative not objective.
Quote from: Malamute Lover on 04/08/2020 00:51:33...Time dilation can be seen to be real when a clock that has undergone acceleration and brought back into a common inertial frame with a clock that has not accelerated. Try restating your scenario with some common inertial frame clock comparisons. ...The acceleration can be taken out for the time dilation analysis.You can see the SR reciprocal thread for the discussion.Have you ever heard about the clock postulate?http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.htmlGamma factor does not include an acceleration,Jano
Quote from: Malamute Lover on 04/08/2020 00:50:40... Are you denying time dilation?...Contraction is relative, not objective....Is the time dilation relative, not objective as well?
Quote from: Halc on 03/08/2020 00:39:04There are actually three distinct scenarios.1) You have a solid ring that spins. It contracts as you spin it. A shrinking ring (that reduces in radius from any perspective) seems awful real to me. Using this scenario, I can pass one wedding ring through another identical one by spinning it. That's real contraction, or it couldn't be done. It isn't observer dependent.You are sort of describing such a thing below, except with superfluous spoke that will bend because they're too long, so they serve no purpose other than to be deformed by being squashed.The geometry of the spinning ring is non-Euclidean. It was not only accelerated up to speed, it is under continuous acceleration as it spins. SR is not a good guide here.
There are actually three distinct scenarios.1) You have a solid ring that spins. It contracts as you spin it. A shrinking ring (that reduces in radius from any perspective) seems awful real to me. Using this scenario, I can pass one wedding ring through another identical one by spinning it. That's real contraction, or it couldn't be done. It isn't observer dependent.You are sort of describing such a thing below, except with superfluous spoke that will bend because they're too long, so they serve no purpose other than to be deformed by being squashed.
The acceleration requires the use of GR. Because the spacetime is curved, the distance from the spinning ring to the non-spinning ring is greater.
An observer on the spinning ring will think the non-spinning ring is expanding so no problem with fitting.
Which is which? As with GR problems in general, who is undergoing acceleration?
But the question can only be settled by bringing the two rings into a common inertial reference frame and comparing clocks, just like with the Twins. It cannot be settled by comparing observations.
Quote from: Halc2) Spoke scenario, or the roller coaster track, which is essentially the same scenario. Here the radius is held constant by the non-contracting straight spoke, or by the stationary track. There is no solid ring, but a series of detached adjacent blocks. If there are spoke, you have essentially a row of independent pendulums. If a track, you have a row of 'bumper cars'. Spin it up and gaps form between the blocks, and more can be inserted if you like.Observers in any frame will agree on this, but you seemingly are in denial of it.The spokes bend.
Quote from: Halc3) The actual Ehrenfest scenario where he takes a non-Euclidean 3 dimensional solid (a spinning cylinder) and declares it paradoxical when its non-Euclidean properties are illustrated. If the object is rigid, it shatters as soon as you attempt to change its angular speed. That shattering is an objective effect that any observer in any frame will witness.Ehrenfest wrote his paradox before General Relativity was developed and did not know about curved spacetime.
3) The actual Ehrenfest scenario where he takes a non-Euclidean 3 dimensional solid (a spinning cylinder) and declares it paradoxical when its non-Euclidean properties are illustrated. If the object is rigid, it shatters as soon as you attempt to change its angular speed. That shattering is an objective effect that any observer in any frame will witness.
Ehrenfest assumed 3D Euclidean geometry, not non-Euclidean as you stated.
He therefore assumed contraction was real, which is what led to his claim of a paradox.
A clock on the surface of the cylinder will run slower than a clock inside the cylinder.
To an observer on the surface (and therefore to the mechanical properties of the cylinder) the same number of revolutions a minute are taking place
An observer inside with a faster clock will be surprised to not see the cylinder shatter just as he is surprised when his Twin comes back much younger than him.
It will be crushed around the circumference. Where does the energy come from to crush it?
Whether and how much contraction an observer will see depends on the observer.
An observer on the spinning wheel sees nothing different because contraction is only visible from another reference frame.
Quote from: HalcQuoteFirst some comments about time dilation. The pilot of a rocket ship that has accelerated to 0.99 c will experience a time dilation factor of about 7. The clock on the ship will be running 7 times slower than before the acceleration.No frame reference, so that statement is ambiguous. It will be running 7 times slower relative to the frame in which the ship is moving at .99c. Not saying you're wrong, just sloppy. It's running at normal rate relative to the ship of course.I did provide a reference frame. The frame in which the ship is moving at .99 c is the one before the acceleration, which I explicitly mentioned right there: “accelerated to 0.99 c”. No sloppiness. We are not going ad hom., are we?
You have to bring two observers into the same reference frame to judge which one is right, that is, which one underwent acceleration.
His observation is that he is traveling faster than c. Known landmarks are whizzing by at 7 c. Why can’t he conclude that Einstein was wrong?
Quote from: Malamute Lover on 04/08/2020 00:50:40Quote from: Halc on 03/08/2020 00:39:04There are actually three distinct scenarios.1) You have a solid ring that spins. It contracts as you spin it. A shrinking ring (that reduces in radius from any perspective) seems awful real to me. Using this scenario, I can pass one wedding ring through another identical one by spinning it. That's real contraction, or it couldn't be done. It isn't observer dependent.You are sort of describing such a thing below, except with superfluous spoke that will bend because they're too long, so they serve no purpose other than to be deformed by being squashed.The geometry of the spinning ring is non-Euclidean. It was not only accelerated up to speed, it is under continuous acceleration as it spins. SR is not a good guide here.The ring is treated as having negligible thickness, in which case it is Euclidean and can be spun up to speed. If not, it is a case of the concrete think poured around the neutron star, making it scenario 3. It shatters if you try to spin it. If already spinning, a thick ring is non-euclidean and does not undergo any angular acceleration.SR describes all three scenarios perfectly, but not the neutron star scenario since that involves gravity.
QuoteThe acceleration requires the use of GR. Because the spacetime is curved, the distance from the spinning ring to the non-spinning ring is greater.It doesn’t matter whether GR or SR is used since spacetime is completely flat in the example, and SR handles acceleration just fine. Spinning a ring doesn’t bend spacetime. It just bends the ring.
QuoteAn observer on the spinning ring will think the non-spinning ring is expanding so no problem with fitting.He will think no such thing any more than anybody thinks the traveling twin made everybody on Earth age faster. He knows very well that his ring is the one spinning and shrinking since rotation is absolute, not relative. Everybody knows it, on the ring or not. That’s what makes it a real consequence.
QuoteWhich is which? As with GR problems in general, who is undergoing acceleration?Acceleration is also absolute. There’s no question what undergoes it. Surely you know at least this much.
QuoteBut the question can only be settled by bringing the two rings into a common inertial reference frame and comparing clocks, just like with the Twins. It cannot be settled by comparing observations.The two rings are in a common inertial frame, and a clock on one runs objectively slower that the other, just as is observed with the ISS.Observation of a clock is completely unnecessary since the one ring passing through the other is objective. You can measure the two rings with a relatively stationary ruler and observe (from any frame) that the one ring is unchanged and the spinning on is contracted. The clocks are more evidence, but not necessary to observer the real consequence.As predicted, you’re just refusing to accept hard evidence. It seems you’re not even denying the contraction now, suggesting instead that the stationary ring might have instead expanded due to the proximity of this spinning ring. No theory suggests any such thing.
Quote from: Halc2) Spoke scenario, or the roller coaster track, which is essentially the same scenario. Here the radius is held constant by the non-contracting straight spoke, or by the stationary track. There is no solid ring, but a series of detached adjacent blocks. If there are spoke, you have essentially a row of independent pendulums. If a track, you have a row of 'bumper cars'. Spin it up and gaps form between the blocks, and more can be inserted if you like.Observers in any frame will agree on this, but you seemingly are in denial of it.
QuoteThe spokes bend.They do not. You have no way to back this fantasy. Yes, time dilation and width contraction varies along its length, but neither has any reason to curve the string, which would have zero effect on that dilation.
The spokes bend.
QuoteQuote from: Halc3) The actual Ehrenfest scenario where he takes a non-Euclidean 3 dimensional solid (a spinning cylinder) and declares it paradoxical when its non-Euclidean properties are illustrated. If the object is rigid, it shatters as soon as you attempt to change its angular speed. That shattering is an objective effect that any observer in any frame will witness.Ehrenfest wrote his paradox before General Relativity was developed and did not know about curved spacetime.There is no curved spacetime in the scenario. Spacetime is completely flat, lacking a source of gravity in the description. He found it paradoxical that a solid could exist in Euclidean Minkowski spacetime that exhibited non-Euclidean properties, but of course SR predicts it.
QuoteEhrenfest assumed 3D Euclidean geometry, not non-Euclidean as you stated.If he assumed the object was Euclidean, then he was mistaken. Spacetime is in that instance, but not the object. No rotating object can be.
QuoteHe therefore assumed contraction was real, which is what led to his claim of a paradox.Contraction being real is what is demonstrated, because it resolves the paradox. The radius doesn’t change because the spin never does. The object was never stationary, and he does not suggest that it ever was.
QuoteA clock on the surface of the cylinder will run slower than a clock inside the cylinder.Indeed. An objective consequence admitted by the guy who denies it. Hmm…How is this real consequence explained if time dilation isn’t real? It isn’t relative since the observer on the edge also sees the clock in the middle run faster.“Neither dilation nor contraction are real, except when I have to admit otherwise”. Great stance.
QuoteTo an observer on the surface (and therefore to the mechanical properties of the cylinder) the same number of revolutions a minute are taking placeNow you’ve contradicted yourself again. We have a stationary marker by which a rotation can be measured. Both observers agree on what one rotation is, but if their clocks are not running at the same pace, they necessarily measure a different time for one revolution.
QuoteAn observer inside with a faster clock will be surprised to not see the cylinder shatter just as he is surprised when his Twin comes back much younger than him.The twin apparently doesn’t know his physics then, because if he did, there would be no surprise. The cylinder doesn’t shatter because it was always spinning.
At this point you go into a bend about gravity and GR, which seems a diversion from the more simple SR topic that you need to master first.
One comment though:QuoteIt will be crushed around the circumference. Where does the energy come from to crush it?It doesn’t take energy to crush something. It seemingly takes force, which means a strong but brittle object can be crushed by expenditure of arbitrarily small energy. The less brittle it is, the more that energy goes into strain and not into failure, so it takes more. I’m assuming insanely brittle and strong materials for our objects else they’d not be able to withstand the centripetal stresses being put on them. Anything else would just fly apart.
QuoteWhether and how much contraction an observer will see depends on the observer.The cases I enumerate above are observed by anybody. They were chosen for that purpose. The measuring rod between ships is also a real consequence.
QuoteAn observer on the spinning wheel sees nothing different because contraction is only visible from another reference frame.In all three cases, the observer on the wheel very much sees differences, which are pointed out in the cases above. You seem to agree that one ring fits through the other, something to which all observers agree. You don’t seem to have any fake physics that lets you deny the bumper-car-track thing, nor do you seem to deny the non-Euclidean dimensions of the ‘cylinder’. OK, the non-Euclidean dimensions are frame dependent. A stationary observer will measure normal dimensions, but the inability of the object to change its angular speed is an objective observation.
QuoteQuote from: HalcQuoteFirst some comments about time dilation. The pilot of a rocket ship that has accelerated to 0.99 c will experience a time dilation factor of about 7. The clock on the ship will be running 7 times slower than before the acceleration.No frame reference, so that statement is ambiguous. It will be running 7 times slower relative to the frame in which the ship is moving at .99c. Not saying you're wrong, just sloppy. It's running at normal rate relative to the ship of course.I did provide a reference frame. The frame in which the ship is moving at .99 c is the one before the acceleration, which I explicitly mentioned right there: “accelerated to 0.99 c”. No sloppiness. We are not going ad hom., are we?It’s not an ad-hom. It’s sloppy because you’re describing ‘what the pilot experiences’ and a pilot always experiences being stopped. You’re referencing the pilot frame and also the original frame, which makes it confusing. That’s sloppy.
Secondly, the bolded statement is wrong since no observer can experience time dilation. I can look at the GPS clocks and objectively notice I’m running slower than them, but I still don’t experience that dilation.
QuoteYou have to bring two observers into the same reference frame to judge which one is right, that is, which one underwent acceleration.Acceleration is absolute (at least in Minkowski spacetime). An accelerometer works inside a box. All observers will agree if something has accelerated. That’s twice you’ve made this mistake.
QuoteHis observation is that he is traveling faster than c. Known landmarks are whizzing by at 7 c. Why can’t he conclude that Einstein was wrong?He is free to propose a different theory, but none has been found so far. So are you a relativity denier then? It seems to be your goal here. You resist it at every step of the way.Such deniers are dime a dozen on sites like this, but then don't go telling me that your stories conform to an established theory and mine don't. I've pointed out several self contradictions with your assertions.Einstein didn’t just suggest that light speed yielded the same value in any frame. That because quite apparent by all the attempts to measure the difference as was predicted by the prevailing view of the time. So he can’t conclude Einstein was wrong, he’d have to conclude that all the decades of light speed measurement were wrong. Einstein didn’t perform any of those measurements.
Quote from: Jaaanosik on 22/08/2020 18:55:37Is the angular momentum calculated in regards to geometric or energy centroid?Center of mass is what counts, which is the geometric center.Per wiki:"angular momentum L is proportional to moment of inertia I and angular speed ω measured in radians per second.[3]L=IωUnlike mass, which depends only on amount of matter, moment of inertia is also dependent on the position of the axis of rotation and the shape of the matter"
Is the angular momentum calculated in regards to geometric or energy centroid?
I guess then the angular momentum appears to be frame dependent because the geometric mass is frame dependent.
The geometric mass is at the center of the wheel for the axle frame and it is shifted for the outside frame.
The outside frame has non-relativistic frames around itself that your calculation should be correct but with shifted center of mass, right?
...That alone has no effect on momentum which is a vector, and vectors are composed of direction and magnitude, but not location....
Quote from: Halc on 26/08/2020 16:01:20[momentum] is a vector ... composed of direction and magnitude, but not location.That's an interesting comment.The vector of the same direction and magnitude but not the location.If the vector is not in the same location within the reference frame then the acceleration effect will be different based on the location. Correct?What I mean is that the outside frame sees the geometric center shifted.If the angular momentum vector is shifted to the geometric center then what happens when the axle, now off center, gets accelerated?
[momentum] is a vector ... composed of direction and magnitude, but not location.