studiot

Thanks Sensei, too late tonight, I will try that tomorrow. +1

So F = μR and R = (in terms of W) ? Can you now make the substitution? When you do you are in for a pleasant suprise. After that I suggest you review both your understanding of turning forces and Free Bodies.

Lots of questions but no answers. Sorry I bothered, I have better things to do.

Click on search button : wait 2 mins Type r : wait 2 mins type e : wait 2 mins That is the problem Yes I have seen this problem with malware in previous versions of Windows, but there are ways to wrest back control of the PC that don't work here. Added to which if I get it to safemode no malware is found dormant. So no I don't think in this case it is malware ((though I will do a proper scan when it is working again) Thanks for this and your other thoughts. Still investigating. It's alway updating these days. Why can't they leave well alone? I am typing this on my trusty XP desktop they stopped messing with years ago. So thanks for all the thoughts so far. I got Skype to work tonight by forcing it to boot into safemode first and then rebooting into full Windows. What a carry on.

We will, but I shall be busy for a few hours now tonight. Meanwhile, Why do you say ? minus mu R rolling friction is F=-μR Have another go at a free body diagram (google it) and only include real forces external to the body concerned.

My Toshiba Satellite laptop, which I principally use for Skype has been misbehaving lately. After booting its response is glacial. Responding to a keystroke can take 1/2 minutes. According to Taskmanager the processor and memory are less than 50% used, but the HD is noted at 100%. The HD is only about half full with about 150GB left. If I force it to boot into safemode (with networking) everything is fine an Skype works, but is useless because the camera and sound are deactivated. The normal mode works once after it has been in safemode, however. I can't see this being a virus competing for HD resources, just one of the Windows screwups. Oh and there is no suitable sysrestore available. Any suggestions where to look for the offending process welcome ?

really ? +1 I thought it was the label.

The torque, yes, What do you think the rolling friction is equal to ? What do you think the normal force R is equal to ? What force do you think that is ? What have you learned from the FBD of the entire car?

Thank you for half a discussion. You were correct I misremembered the equation, but you did not answer my comments. So I can take it you are avoiding saying that when you multiply a tensor by a constant you get another tensor.

Isn't techology wonderful when it works ? Until it doesn't. I see there was a glitch in my last post. The scan gave you the correct equation (Newton's second Law) for the acceleration, but was cut off at the knees. My edit/correction I see missed off the acceleration completely. Sorry. So here we go 4F = W/g times acceleration or acceleration = 4gF/W So now we need to find a value for F. Which is why we need a free body diagram for a wheel ?

I second this. +1 You might like to look at 'the point at infinity' in relation to complex numbers. https://en.wikipedia.org/wiki/Riemann_sphere

Whilst I am not unhappy with the framework idea in your description - There are plenty of pictures of multidimensional 'singularity' arrays on the net, but I find one or two inconsistencies between your OP and later statements. Madelung theory is about as far as you can get from unreactive since it is basically the sum to infinity of multiple (but diminishing) charge interactions. Pilot waves are less interactive, but they carry momentum and are neither singularities nor asymptotic. I see no connection here. You also need to explain why pressure makes any difference to something that is absolutely unreactive. As an alternative to a multidimensional array of needles, you might like to look at Cantor Dust https://www.google.co.uk/search?source=hp&ei=WXfOXcv-H46mUIm7hdgH&q=cantor's+dust&oq=cantor's+dust&gs_l=psy-ab.3..0j0i22i30l7j0i22i10i30j0i22i30.846.3822..4576...0.0..0.300.1868.6j3j3j1......0....1..gws-wiz.......0i131j0i10.uOpLkawVaVI&ved=0ahUKEwiLj4fl-uvlAhUOExQKHYldAXsQ4dUDCAc&uact=5

Once again, thank you for the honest answers. 1) No, just because some of the entries are zero, does not mean they don't exist. Can you demonstrate a rectangular matrix with only 10 entries that is also a tensor? 2) So are you telling me that you can add a single real number to a tensor or are you telling me that when you multiply all the elements of a tensor by a single real number you don't get another tensor? If you want to use a 'cosmological' constant you have to apply it everywhere, which means you multiply gυν by it. 3. SR is only global in the absence of all mass and energy in the system. 4. Thank you for that confirmation. So can you reference a clock that can directly read time units in this system, and what does it read? (perhaps swansont will help here - this is his field not mine.) I would also respectfully suggest that adopting this practice whilst saying nothing is baffling for many members here who may be unfamiliar with natural units in general and geometrised ones in particular. https://en.wikipedia.org/wiki/Natural_units https://en.wikipedia.org/wiki/Geometrized_unit_system

Addendum I think you are working in so called Natural Units when you post these formulae and say that the interval ds = proper time so that c = 1 Is this the case please?

Thank you for the reply, I think it is more complicated than this, and in particular gravitation was not the only variable I had in mind. The metric tensor you mention is a 4 x 4 array with 16 coefficients (in 4 dimensions) and describes the coordinate frame being used to measure the interval between events. This is because it is based on the general quadratic ds2 = g11(dx1)2 + g22(dx2)2 + g33(dx3)2 + g44(dx4)2 + 2g12dx1dx2+ 2g13dx1dx3+ 2g14dx1dx4+ 2g23dx2dx3+ 2g24dx2dx4+ 2g34dx3dx4 Which you will note has only 10 terms. Thus we have 10 equations and 16 coefficients. So there are many ways to make the reduction to 10 coefficients. Of course a general equation of a higher power could have been chosen, resulting in even more coefficients. But we have no evidence (or even perhaps the means to make supporting observations) for doing this. Higher powers seem to have negligeable effect. But this is the Remanian geometry of GR and the g coefficients themselves are not real or imaginary constants, they are themselves functions of the coordinate axes. This geometry applies globally. In SR we can reduce this further to the 'flat' Euclidian geometry of the four squares. This geometry only applies locally. Having set the scene let us look at the Field equation(s) where this tensor is used. The metric tensor premultiplies the 'Energy-Stress' tensor which contains elements describing the distribution of energy, mass and momentum. However there is yet another term in the Field equation - the Lambda tensor, which is not affected by the metric tensor. So even if you reduced all the g coefficients to zero, reducing that term to zero, the Lambda term would remain.

Dir you mean SR or GR ? The equations of GR refer to other properties than elapsed time and length (what clocks and rulers measure)

You will get considerably more than that, depending upon the actual edition you buy.

That's a fair question to consider so let's try. Suppose we do without the second postulate. What are the logical consequences? Why should light behave in any way differently from sound or rockets or other physical entities in motion? If that were the case then would that contravene the principle of relativity or are the two principles independent? The short answer is no it would not because they are independent. Einstein himself realised this and noted It is this meticulous checking through the logic, here and elsewhere in the paper, that makes Einstein's derivation longer than most modern ones. Naturally he then goes on to prove the compatibility of the two axioms. Remember that the principle of relativity was not revolutionary and had long been known. It was the second (light) principle that was the breakthrough. Does this help?

A free body diagram isolates any body or part of a body from the rest of the universe. It shows the magnitudes, positions and directions of all forces and moments exerted on the body by the rest of the universe. It does not show any forces exerted by the body on anything. The vector sums of these forces and moments are sufficient to maintain the body in whatever state of motion it is in. We can establish sums of the forces in 1,2 or 3 dimensions independently. If the sum in any dimension is zero the body is in equilibrium in that dimension. If the sum is not zero the body is accelerating in that dimension according to Newton's second law. If the moments in 2 or 3 dimensions are zero the body is in rotational equilibrium in that situation. Here is a free body diagram of the car as a whole, with a couple of realistic assumptions about weight distribution. See how simple it is ? Following this example can you do the same for an individual wheel ? Sorry I see that the bottom of the scan did not come out properly the equation should read 4F = W/g

I think I can- but it's really not that simple when there's so many parts here to consider. It is that simple. Simplicity is the purpose of free body diagrams. It simply moves (accelerates uniformly with this unknown yet constant acceleration) in the right direction as the picture suggests. So it's not moving upwards/downwards- just rolling without slipping You have stated no equation balancing forces here ? we assume here that this motion is in the right direction of this horizontal plane. So I think we can say that the equilibrium is met here. Again no equations? This one is the crux of the problem. I drew here a non-inertial case of this vehicle in motion - so ma would be the force that it takes to keep the motion going, I thought and hoped you knew better than that.

The driving torque is determined by the engine/transmission, not the conditions where the wheel meets the road. When driven in a straight line: For any given driving torque we have that the frictional force times the wheel radius times the number of driven wheels = the driving torque up to the point where the wheels start to spin. Look at your first diagram. Is the vehicle in vertical equilibrium (is it moving up or down ?) Is the vehicle in horizontal equilibrium (is it moving left or right ?) So what net forces are acting on the vehicle? This must therefore be the accelerating force on the vehicle. Can you complete this ? In your second diagram, what does the blue arrow ma represent? Do you know how to construct a free body diagram? Edited just now by studiot

A circle is the locus of the path swept out by the end of a rotating arm of constant radius. But that radius, though constant is not invariant; I can trace out different circles, spirals etc by altering the arm length (radius).

Actually the first recorded words were due to

But among that infinite number it is quite easy to make a choice. If one assumed that some theory beyond GR, say QG, will define an absolute space, one would have to specify equations which distinguish absolute space, thus, a condition which would distinguish the preferred coordinates. But there is essentially only one candidate for such a condition, namely harmonic coordinates. And there is also a single distinguished set of such particular harmonic coordinates, namely the comoving coordinates of the FLRW ansatz. For zero spatial curvature, which is what we observe, the FLRW ansatz would be ds2=dτ2−a2(τ)(dx2+dy2+dz2) , and the coordinates x,y,z are harmonic. Absolute time would have to be harmonic too, but this is also not difficult, the slightly modified ansatz ds2=a6(t)dt2−a2(t)(dx2+dy2+dz2) has already a harmonic time coordinate too, so that harmonic time and proper time are connected by the simple equation dτ=a3(t)dt. This would be the only choice where the Copernican principle holds, with no center of the universe. So, to make a plausible choice among that infinite number is very easy, no trouble at all. A word of caution here. The OP of this thread based his disscussion of 3-Momentum which is frame (observer) dependent. And that will have been the background to Strange's comment. Your equations pertain to 4-Momentum which is quite a different animal, used and understood by many of the other participants in this thread.

The relativity chapters in this (free) E- book might help https://static1.squarespace.com/static/544a8c3de4b03e16957ae263/t/54b6d789e4b0a3e130d1e7cc/1421268873531/Nolan_Modern_Physics.pdf This 2019 book comes from Peter Nolan's lectures at NewYork state college a couple of years ago and has lots of useful background and diagrams not usually offered.