studiot

This is off topic here so I shall not refer to it again, just refer you to this article in Poinsot's Theorem and Wrenches in Mechanics. If you wish to pursue the difference between 2D and 3D please start another thread where it can be discussed at leisure. http://www.cs.cmu.edu/afs/cs/academic/class/16741-s07/www/lecture14.pdf Yet other French Mathematicians associated with differences between 2D and 3D are Varignon and Poincarre. You have already accepted movement is available in the OP. I know of nothing in General Relativity to suggest that movement is necessary to establish the apparent force of gravity. If there is I would be very grateful if you would point it out.

Now that we have agreed the conditions which the OP set, we can move on to the question he actually asked, and MigL offered an analogy in a simplified situation. The question that was asked boils down to Why do objects subject to gravity experience an apparent force if gravity is due to (some form of) curvature? Well Migl offered a situation where objects would indeed experience an apparent attractive force, although none really exists, due to the curvature of the 2D manifold and not due to any gravity. You come from the land of imaginary forces (D'Alambert) so you should not be so suprised at this. As to your last line, we are discussing the classical mechanics of angular momentum in another thread here and are approaching the point we we can deduce that even the simplest multidimensional system (3D) have properties that do not exist in 2D, so perhaps you would like to reconsider or rephrase this?

Actually he doesn't say anything of the sort, however since I know that neither you nor he have English as a first language I will explain a best I can. He actually said He did not say the system was at rest, just that any motion of the large mass is follwed by a comparable motion of the small one. One of the tenets of Relativity is that there is no such thing as absolute rest. I'm quite sure MigL can answer for himself but just remember he was trying to reduce an extremely difficult problem (visualisation in 4 dimensions) to a simpler one to promote understanding. Yes his model is not perfect, but it is very clear.

Welcome to Science Forums. You should definitely start by reading this here. http://www.scienceforums.net/topic/75772-read-this-before-posting-in-homework-help/ and then following the instructions. What have you done so far towards the problem?

I suppose some fool has to wonder if applying the relativity of the Twins doesn't mean that no two particles have the same age, whatever that means, since no two particles can have had identical trajectories through spacetime.

Avoid marble or concrete (I think you call it cement). They are not acid resistant. Natural stone can't usually be finished to a sufficiently fine surface. Artificial stone is usually fabulously expensive, but can be effective as others have said. Epoxy or polyester resin with ground silica / mica / corundum filler. Corian is very good and relatively lightweight. A cheap alternative for the home might be resin faced shuttering ply, which is pretty hardwearing.

To move on to angular momentum and examine the question ‘what is angular momentum?’ I am going to go back to statics and my post#64 So consider a general force vector as in Fig 1. Like all vectors, F acts only along straight lines, shown dashed in the figure. F is both the force and its point of application. Introduce some general points, S, T, U and W in Fig 2. The moment of F about a general point is defined as the product of the perpendicular distance from the line of action to the point, as shown. Note that there does not have to be any physical object at any of these points. If there is a physical connection between F and the point (say S) about which the moment is taken then that moment is applied at S. Otherwise the moment is notional, but still exists mathematically. Fig 2 also shows some particular points. 1. The magnitude of the moment is, in general, different for every point. So the inequality shows that the moment about S is numerically different from the moment about T 2. The direction of the moment is clockwise or anticlockwise depends upon which side of the line the point lies. 3. The moment at U has the same magnitude and direction as the moment at S and U lies on a line parallel to F. So moments are only the same if they lie on a line parallel to the line of action of F 4. The moment at W is zero or does not exist and W lies on the line of action of F. Fig 3 shows that if, instead of a force we apply a couple at F we find that 1. The couple exerts the same turning effect about every point (including S, T, W and U). 2. The couple has the same direction about every point. 3. There are no points with zero moment. Quite different from the turning effect (moment) of a single force, as promised. I will not prove these unless you specifically ask, although it is an easy proof to demonstrate. A real world physics demonstration of this can be had by loosely nailing a plywood lamina to a post and comparing the turning effects of a single force via a spring balance with the turning effect of a large screwdriver, both applied at various points. A further important difference is that a single force acts asymmetrically, a couple can only be realised by a pair of forces or multiple pairs of forces, which then act symmetrically. The ultimate being an infinite number of pairs or a ring force as found in a rope round a capstan or windlass. I have mentioned symmetry because it connects directly with Noether’s theorem that Mordred referred to. Noether was a very theoretical Mathematician and it is pleasing that her theorem (1918) manifests itself in physical reality but there is no reason to expect physical reality to follow modern theoretical mathematics. There is plenty of such modern mathematics that has no physical counterpart. Earlier Mathematics was structured to follow physical reality. Force is a vector and if we now replace this vector with another one, either velocity or linear momentum we find what is known as ‘moment of momentum’. This is an instantaneous quantity and the point it is taken about is called the instantaneous centre. For a general motion this will change with the motion of the body at F. It is unsymmetrical, like the moment described above and in the same way that the moment changes, the moment of momentum changes. But I mentioned two modes of turning motion and the second is called spin. This corresponds to the couple in statics and is a symmetrical mode. A spinning body possesses angular momentum S, by virtue of its spin as well as moment of momentum by virtue of its translational motion. Its total angular momentum is then the (vector) sum of these. Hence my previous comment that there is an extra term in the equation. We can explore a simplified version of this in the next instalment and find out the conditions that lead to conservation of total angular momentum and also the complete muddle that modern presentations have got themselves into. We can also explore why adding couples and the moments of forces in the first part is simpler and easier that adding moment of momentum and spin. Now that we are on better speaking terms I'm sure there must be questions, don't hesitate to ask.

Thanks Moontanman, I've not seen the first one before. Don't forget that this sort of effect has been put to good use in things like the impellers driving sealed pumps. +1

No. In the first place the radiation of an EM filed is a classic wave effect, and only occurs when the charge is accelerating. In the second place the emission of a photon is a quantum effect and in this case there is no emission dues to acceleration. For instance the electron does not spiral into the nucleus, loosing energy by emitting photons. The emission of EM waves is typified by the X rays emitted by a cathode ray stream, accelerated in a vacuum tube. The re is obviously a relationship between the X rays and the elctron stream, but it is not quantised. Here is a nice gif of the emission of EM by a moving charge, courtesy NASA.

But maglev requires a dedicated track. That is the whole point. No one system is perfect and the best one deopends upon a tradeoff of benefits and disbenefits.

Both your statement "where it was before" and Eise's It will deviate from the time axis imply an absolute axis. In Eise's case the phrase 'the time axis' In your case where 'it was before' give the game away. Ignoring the fact that you cannot simply 'add a mass' think of it this way There are two different situations being compared and measurements in one system cannot be subtracted from measurements in the other to say 'it moved'. The system with one mass has a different coordinate system from the system with two masses, they can never be the same. There will be a third system to which you can reduce both the original scenarios, and in which you can say 'it moved' But then again there will be many others in which 'it moved differently' is appropriately and finally possibly one in which 'it did not move at all' All these systems are equally valid, that is the point of relativity. Gauss' Theorema Egrerium says that the measure of the projection of the comparison is invariant in all manifolds.

Once again this analogy is fatally flawed as is implies there is some absolute reference underlying both the gridlines and the object's 'true ' position. There is no absolute reference to say that 'it moved'.

As quiet as a hovercraft no doubt.

Well I had a great professor of spelling.. name of Molesworth.

Like it, MigL +1

Nevr reread over one of your old posts. It just makes you cringe how crappy your spellung is.

I am going to go right back to the beginning and start again. I shall work through your proposition a line at a time trying to knock it into proper shape so you don't end up with fallacious conclusions. You are welcome to come along for the ride, you never know you may learn something to your advantage. So the first line "Both angular momentum and momentum are accepted to be conserved values" This, like many of your statements are half truths. I am sure this is unintentional and based on inadequate study material. Are accepted ?? by whom ?? Are conserved values ?? Always?? What is meant by a conserved value in this case?? I am glad you mentioned linear momentum as well as angular momentum as I can start with linear momentum. This is much easier but clearly points the way to go. A point to remember that will become important further down the line. Both linear momentum and angular momentum are vectors. Vectors have magnitude and direction. So to be conserved both magnitude and direction have to be conserved. Let us consider a fairly general system of particles which comprises our system for analysis. This may only be a single particle or it may be many, operating as a single unit. The centre of mass moves as if the whole mass of all the particles were concentrated at this point. The motion of this centre is completely independent of any internal forces (internal forces are those acting between the particles) since by Newton's third law every such action is countered by an equal and opposite reaction. If M is the total mass of the system and FE the external forces then by Newton's second Law [math]\sum {{F_E}} = M\ddot \bar \alpha = M\frac{{d\bar v}}{{dt}}[/math] I note that there is already confusion between you and Mordred on the meaning of the symbol r, which is why I asked you to define your symbols before. By convention r is used for a position or displacement vector, not radius. In either event I have used the greek letter alpha to avoid confusion. In any case we can quickly move away from this variable. The equation states Newton's second Law that the sum or resultant of the forces equals the total mass times the acceleration, where the acceleration is the second time derivative of the position vector alpha. This is shown by the double dots over the symbol. The symbol also has a bar over it to show it refers to the centre of mass position. OK That was a big chunk, now for the cool bit. In the case where the vector component of the forces in a particular direction is zero [math]M\ddot \bar x = M\frac{{{d^2}\bar x}}{{d{t^2}}} = 0[/math] I have taken the x axis to be in this direction so moved away from alpha as promised. This is a very simple high school differential equation which when integrated (solved) has the solution [math]M\dot \bar x = M\frac{{d\bar x}}{{dt}} = M\bar v = {\rm{a}}\;{\rm{Constant}}[/math] and [math]\bar v[/math] is the component of the velocity of the centre of mass in the x direction. This is hugely significant because Mv is the component of the linear momentum of the system in the x direction and it is constant. Constant means it does not change and we have fixed the x direction. So this is a form of conservation for linear momentum. But it only works because a term in our equation of motion is zero or null. It is not true in general. This type of 'conservation' is called a null based conservation. [math]{{\rm{p}}_x} = M\dot \bar x = {\rm{a}}{\kern 1pt} \;{\rm{Constant}}[/math] Where Px is the linear momentum in the x direction. That is enough for now, but I can tell you that conservation of angular momentum is similarly based but the derivation is more complicated as there is another term in the equation of rotational motion to consider. How are we doing?

First I would like to nominate this post as a shining example of the right way to introduce some scientific news or announcement for discussion. It contains not only the announcement but a short synopsis or summary of the material of sufficient quality to gauge the nature of the news. This is then followed by a link to a much longer original source material for those who want it. +1 As to the news itself. It is still early stages of an investigation, too early to believe or disbelieve the conclusions offered. I see there is, as yet, no independent verification of the alleged sapiens bone fragments, either in dating or being from Homo sapiens. I therefore look forward to reports from this next stage investigative stage. Too large a conclusion is drawn from previous knowledge that cartain types of stone tools are found widely distributed in Africa, coupled with this find. Until the other sites with these tools are shown to have been inhabited by sapiens, this is evidence from a single instance so cannot be counted as evidence of widespread location of sapiens 'throughout the continent'. No does it rule this proposal out. It is simply not enough either way. An alternative springs immediately to mind. North Africa was much more hospitable in those days, much of this has been washed away in the sands of Osimandias. So it is conceivable that somewhere in North Africa the sapiens started and spread, perhaps both ways. What we are finding are the remnants of this with the middle parts destroyed by the ravages of time.

In which case can we please follow the rules of this forum in which the promoter either completely sets out his stall in the first post or defines his terms in subsequent answers to questions about that which is missing from the opening proposal. I have asked repeatedly adn without success for proper definitions of all terms employed, the scope of all equations used and a full and accurate description of at least one system conforming to the proposed analysis.

Thank you for replying at last. Yes you can incorporate the drive in the track/vehicle system, but that confines the vehicles to special tracks exactly as I said. You need special tracks not only to provide forward propulsion but also to prevent sideways movement and to guide the vehicle around curves and intersections. How would a crossroads work? An important point about wheels is that you automatically get traction from the frictional contact with the roadway or even (especially in the american case) off-roadway surface.

I still don't think the OP has appreciated it's a whole lot worse than that. Assuming for the moment that you have levitated your vehicle by some means. What are the ways of propelling it? Propellor/TurboFan Jet engine Rocket Engine Have you ever stood behind a hovercraft fan or saturn rocket exhaust or any other of these? There is a real issue with other such vehicles on the road, even in perfectly windfree conditions. And yes, as Halls of Ivy said How do you stop, manouver etc?

I thought I would try to track down the original quote and I ended up here, where I have to say there is a more wide ranging discusion. https://www.quora.com/What-did-Einstein-mean-when-he-said-Science-without-religion-is-lame-religion-without-science-is-blind-And-do-you-agree-with-him One particluar (short) response sums it up Please note the entire article is reproduced as well as detailed information on the history and circumstances surrounding it.

Why would I ask you? I'm sorry if my intent was unclear. I do think that not understanding this difference may underlie Mandlbaur's difficulties. You are welcome to explain if you like, particularly as he won't talk to me for some reason.

Yes, I'd add +1 to Kip as well. But I'd also add that Kip's agebra works mass concentrations, useful now that we know we are talking about a food recipe. You did post this in Inorganic Chemistry where a Chemist might be forgiven for thinking molar concentrations, and why not organic chemistry for food?

There is a subtle difference between angular momentum and moment of momentum. Do you know what it is? Hint it corresponds to the differnce between a couple and the moment of a force.