Centrifugal Force Demo:

**CENTRIFUGAL FORCE**

**THE GREAT UNKNOWN**

Shortly before he died, I sat with him so that he could explain his theory of Centrifugal Force, “The calling card” as he called it, for the millionth time. This time, however, with a tape recorder.

By sheer luck, or bad luck, I only have 1 hour of recording, but that’s better than nothing as you must always see the glass half-full rather than half-empty.

The story begins like this…

*“All my life I’ve had a great scientific curiosity for the unknowns and problems in nature and this has led me to investigate the multiple unknowns that have encircled nature throughout my life.” *

I’ve continually kept myself informed of the latest advances and discoveries in different branches of science from publications. What has interested me above all is everything to do with macrocosms and microcosms and I have even considered those possibilities which certain eminent scientists have expressed which may be called philosophical-science.

I combined this with the attraction I’ve always felt for experimenting with many of the laws of physics, even the most elemental ones so that they would corroborate each other. I discovered a branch which fascinated me, without leaving anything else aside and I dedicated many years of research into the phenomenon of MAGNETISM. More than just the phenomenon itself but its manifestations and quantification. I searched numerous publications about this for a long time, keeping myself up to date with not just the academic part from textbooks but also the latest developments and advances in magnetism.

The truth is that many of the claims made in the many books and articles… besides some simple ideas which everyone can find out about the lines of magnetic force, the famous iron filings experiment, where they arrange themselves into a classic shape on the paper when a magnet, a magnetic force, is placed below the paper and the filings rearrange themselves into a specific shape at the poles, as if they wanted to go from one pole to the other in a type of curve called ellipses.

Besides this display of something intangible and invisible, the lines of magnetic force are invisible, there are many laws of this type. I analysed them a little and I focused on the permanent magnet and its explanations (magnetite) and those defined as “Weiss Domains”. These are domains where the molecules arrange themselves into a shape where they acquire a privileged direction from one pole to the other. The same shape as either a permanent manmade magnet composed of ferrous materials or alloys and the use of induction (a coil with a current passing through it thus producing a permanent magnet due to the phenomenon of magnetic induction as once the current is removed, the bar remains permanently magnetised) or natural ones. The educational part talks about its quantifications, the formulas which govern these phenomena but I’ve always wanted to ask the question WHY… why is this so and why?… and generally this cannot be explained by textbooks not even those specific to magnetism.

I thought that the basis on which magnetism is finally governed was due to its handling, in part anyway, by the spin of the electrons around themselves. This electron spin, which is like a revolving spinning top, generates an electric current and a magnetic field at the same time due to a well known law of 3D – the law of 3 orthogonal directions – among others.

After having studied these principles from different angles, I considered that if that were due to the electron, it didn’t explain how this arose and what the state of the magnetic fields was.

After analysing and thinking about this, I let my imagination go wild and for several months I tried to find another different explanation from the official one mentioned in the current books.

In this way I realised that there is more to magnetism and its primordial form on which it’s based than what we’ve been told.

I believe that nature sometimes behaves like those Russian dolls which as you open them up, you find another smaller one inside, and so on successively. It makes you think that nature likes to unveil her secrets and mysteries little by little and that some lead us to others and so on… and as such I started to think that there may be another manifestation of nature behind magnetism that we hadn’t yet discovered or that there was some other different consideration than that which had been put to the test scientifically or made public. Quite possibly many scientists who had studied this field knew much more than what had been made public so that fans or even students could access this.

Despite searching for many final or definitive explanations about what magnetism is, I wasn’t able to find any explanation to fully satisfy me or my curiosity.

What did take place after all this investigation and consideration that arose after 15 years of verification, summary and compilation of all the data, is that I seemed to understand or have a gut reaction that magnetism wouldn’t exist if there wasn’t a certain movement or at least a certain variation in direction.

This led me to believe that some type of magnetism could be linked to movement. But, which part of physics is movement studied in? DYNAMICS.

I began to study dynamics, movement related to magnetism. Whilst books didn’t give me the absolute precise and perfect solution, I saw that not only the formulas but the explanations which encircled the concepts could be joined together and that this could be joined with some type of direction change which is no more that a spin. From this point the idea of spin came to my mind and people think it’s a circle, but at an infinitely small level, a spin is a change in direction.

Already disappointed with my research into magnetism I changed direction and started studying dynamics as I mentioned, and I found a uniform circular motion and lots of other types of movement besides that. I focused on this which in turn is nothing more than a change in direction and as a result, I soon stumbled on CENTRIFUGAL FORCE as it had been called for some 40 years or so.

Urged on by my natural spirit of curiosity I started to work on centrifugal force. I looked for all the literature about it both in textbooks and in other books in which it was implicit in certain phenomena.

The first thing I found was its formula

CF = m.v2 /r

This is the most basic formula but the more complex ones are basically the same underneath.

There was a lovely but basic experiment with vectors in which there is a centrifugal and a centripetal force. The textbooks told us that one didn’t exist without the other opposing one. Both acted at the same time and when one disappeared, so did the other. The vector experiment at that time denominated it as a centrally seeking force. The classic example is an object tied to the end of a string which is maintained fixed and the object is made to spin around. When the string is cut, the object leaves at a tangent, the tangent being at the point where the central force has been cut and, as a result, you are cutting the centripetal force. In this case, the centripetal force which is shown in the joining axis or radial between the centre and the end of the string with the weight, makes the forces vanish and the weight leaves in a tangential direction from this point and at the lineal velocity which it possesses. However, during the time in which it has been revolving around the centre, it has generated a tension in the radius which is in fact the manifestation of this famous centrifugal force.

On doing this elemental vector experiment, all of them, the small arc degree or spin angle and the string with the arc are exactly the same. It is also the same as the arc belonging to the circular trajectory with the string which results in a straight angle on the radius. Imagine the angle ‘alpha’ to be infinitely small but not ‘0’. Why different to ‘0’? Because if ‘alpha’ = ‘0’ we wouldn’t have any movement. At the opposite end of the arc angle, the arc and the string could be considered practically the same as the difference, so small as to be considered negligible, if it is made infinitely small.

This infinitely small calculation takes us to calculus, beautiful calculus which gives us some equations to find out the equation of a curve. In fact, what we know is the equation for infinite points close together but as the size of a point is ‘0’, there is a minute distance between one point and another. The calculation is deduced by a difference of rectangles corresponding to the small and minute distance between each point. In practice, the books say that differential calculus is approximate but valid for real life calculations. It’s almost perfect, but we mustn’t forget the word ALMOST – it isn’t 100% correct.

This was the concept employed in the vector calculation of centrifugal force assuming that the arc belonging to an infinitely small angle which is not “0”, is the same as that of the string that underlies it.

Having stated this it can be clearly seen that however small angle alpha may be, the difference between the string and the arc are extraordinarily small but not “0”. However, by having to multiply these minute differences in the calculation, you have to multiply the angle by a million minute differences given that it has been divided into a million pieces which results in a million minute differences. It could be that these differences may mask the truth from us or don’t give us the result or exact proof of what we consider centrifugal force to be.

I made many calculations here contemplating small angles and looking for all the tangents at different points in this minute angle and getting different results. Thinking about a large or small arc, by multiplying them by the corresponding pieces in which this angle has been divided, the results differed notably.

So it was like this in those days that I thought that this experiment was approximate but possibly not precise. Over the following years, they started to alter the claims made about centrifugal force in the textbooks until about 12 years ago, between 1990 and 2000, when they started to call it a fictitious force. At this moment I thought that all my experimentation and deductions might be going in the right direction given that if official science was doubting its accuracy, I couldn’t be far off the mark.

In some more modern textbooks after 2000, the student or whoever it was who were to use the centrifugal force formula was advised not to do so as, according to the book, it contained some quite worrying calculations which were imprecise or even had mathematical errors.

From that moment on I thought that I could continue to pursue in depth some of those thoughts I’d been having during this time and try to organize my ideas about this topic.

Where did I start? I started with the fact that a body joined by a radius or an axis or central point and which spins around leaves exactly tangentially or in other words at 90º in relation to the radius. In addition, its direction leaves at 90º which denominates the tangent of that point and at the exact velocity it was travelling, the velocity hasn’t changed. I said to myself that we’re going to start from the end, so I take a radius, a central axis and a weight at the other end of the radius which is revolving and at a precise point I let the weight go. What happens? The weight leaves at 90º from the radius release point which held it fast to the central point. It leaves tangentially and in a straight line at 90º from the point where the radius held it. The weight advances a minute amount as well as the radius at the speed it was travelling – assuming its weight or size insignificant – but it has also spun – assuming the size of the radius doesn’t change. The weight moves forward in a straight line and the radius revolves by a small angle alpha, this time with no weight. What geometric shape do we find? If we joined together the angle where the weight is found and where the radius is found, we see that the 90º angle has opened up or in other words the angle is 90-point something degrees.

Remember that physics tells us that no 100% rigid natural bodies exist so the radius, when there’s a weight at one end and is revolving tends to lengthen slightly due to another law of physics, and I think that this is true. If the radius has increased in length slightly so the starting length R0 is smaller than the final length Rfinal gives us an angle alpha sub 1 which is greater than 0 and a longer radius than R sub o which gives us a fictitious angle because we have released the weight, between the weight travelling in a straight line and the lengthened radius.

Let’s imagine that it’s lengthened, it remains attached but it’s lengthened. What happens now? Why do the materials stay joined together? We said that there aren’t any rigid bodies but the radius which held the weight is a solid body and we know that it remains solid due to molecular bonding. What’s happened in the radius that’s been lengthened? Clearly, the bonding forces between the molecules making up this radius have eased minutely?? and the distance between the molecules has also increased so that R1 is greater than R2. Bonding forces, however, are elastic – think about an elastic band or a spring – and as such, having increased this it has increased sufficiently for the pull on the weight to cause a release angle of 90º and increase it to 90 point something degrees. This resulting force which as it varies causes the bonding force exceeds the tension force produced by the lengthening of the radius, and at that precise moment, the weight returns and remains in the R0 dimension of the radius, but as it happens in a moment of time, there’s another law of physics that says forces do not act in time ‘0’, or that instant forces do not exist if we remember the formula:

Mechanical impulse = size of movement

Force x time = mass x velocity

If time were zero, all the formula would be zero and as a result, this happens in a minute interval different from zero too. The straight line there was at the beginning, the perpendicular of the tangent the weight left by, and later the new one, is straight. This back and forth when the weight returns from blow R1 returns to R2 does not happen in a zero instance of time as thus the exit straight line is not entirely straight and is a type of curve but not a circumferential arc in both the forward and backward motions. In this case, the two arcs are from a hyperbola and as such, we can assume that the weight has produced not a circumference arc, but a minute, infinitely small hyperbolic curve during a small duration of time. It left R0, became greater than R0 and then returned to R0. It has plotted a hyperbola from both its exit point as well as its arrival point and these two points are tangents and separate. The exit point is a tangent which will be the start of a new point of the separation start with a 90º angle. This point is the only one with a 90º angle between the weight direction and the radius, and from then on, it will return to increase and the aforementioned ideas will return to take place causing another exit semi-hyperbola and return semi-hyperbola at radius R0. What shape will appear if we continue like this? We’d have in place of a circumference, a shape made up of small, hyperbolic undulations with the initial radius R0 at its lowest point and at its highest, the apex of the hyperbola. After making a series of mathematical calculations and applying a formula I deduced, it turns out that there’s a point X between the circumference arc and the hyperbola corresponding to radius 0 and radius R1. There is a difference X where the difference between the maximum apex of the hyperbola and the corresponding circumference arc, and this distance X is the point which we can assume to be the place where there was centrifugal force, or what we believe to be CF, but this point is located outside the circumference and a little above the radius R0 and a little below R1. This point is equivalent to the sum or statistical calculation of the vast amount of molecules, not infinitely so, which can be found at different distances and not all the radius are R0 and R1. It’s a fictitious point and where all of the mass of the body is assumed to be concentrated, but the body is somewhere around this point and the centrifugal force around this distance R0+x.

So it can be deduced from all this that while the body has been revolving, the radius has always remained, or in other words R0+x is greater than R0, while the radius has always been longer than the original radius and this radius is the one where this so-called centrifugal force has been applied or manifested itself.. This force is effectively composed of 2 parts – centrifugal and centripetal forces: the former wishing to leave and the latter wishing to attract towards the centre or towards the tangent of the circumference from the starting R0. The tiny interval X which increases by R0 is not contemplated in the well known formula, which shows a conceptual error because when the body revolves, the size of the radius increases.

We’ve discovered a paradox where uniform circular motion couldn’t exist and actually it’s the result of the average of all the different hyperbolas of the molecules which the revolving body is composed of and whose centre of mass is found slightly further from the centre where it started.

Having made the calculations and pertinent formulae, centrifugal force can be expressed in my final formula:

CF= mass x velocity2 / r0 x Coefficient X which makes r0 slightly longer. As a result an index is missing from the formula and logically and by definition it must be greater than R0.

Once the body has stopped moving, it’s assumed that it returns to its original length. I reject the possible deformations due to the phenomena of molecular bonding, material resistance, elasticity and many more. We’re talking about a purely theoretical shape.

– End of recording –