Session 1 First steps in Physics



First Ventures into Physics

Studying Physics in the1950’s filled one with excitement; Calder Hall was starting to harness Nuclear Power, the structure of DNA had been determined, Lasers and Masers were being talked about, transistors were replacing valves in electronic circuits and Space was emerging as the final frontier. As early as 1945, Arthur C Clarke (Extra-Terrestrial Relays, page 305, Wireless World, October 1945) had given us the elements of satellite communication and, by 6th October 1957, Sputnik 1 led the way for countless other space vehicles- what new challenges lay ahead?

I label myself as "pre-war" and in hindsight it is obvious the WW II had left many exciting scientific and technological marvels in its wake. The German V1 and V2  bombs established rocket science and technology; Radar led to Radio Astronomy and huge advances in communications; the code breakers at Bletchley Park set computation and programming on a firm footing and the nucleus was revealing its secrets in a most violent manner. I was lucky to have an older brother who shared in the excitment of post-war Britain and he inspired me to be curious about both the natural and man-made world. On building a crystal set at an age of 8, or so, I was fastinated that it "sprung into action" and sound came out of an earphone. A few years later I was riding round the fields at home on a small motor cycle and I marvelled that the machine could convey me anywhere I wished to go when turning the twist-grip --

                                                  what was the magic of wireless and engines?

Well, more than five decades on, this wonderful subject called Physics is not held in such high regard but we still need to have an appreciation of the natural world so here is just a short section which may engender some enthusiasm for a subject rich in history and diversity.

What makes things “tick” has always excited the curiosity of Homo sapiens and man does appear to be distinguished from other animals by his great store of imaginative gifts. He makes plans, inventions, new discoveries, by putting different talents together. Discoveries become more subtle and penetrating as human beings learn to combine their individual talents in more complex and intimate ways and society has built on what previous generations have bequeathed, to build an ever-increasing store of knowledge and artefacts.

From early history only two important “discoveries” will be listed to show the time scale of the development of the human race.

Mankind has used fire for about 400,000 years and this has allowed changes from Stone Age to Bronze Age to Iron Age.

The wheel is thought to date back to about 3,000 BC (5,000 years ago) in the form of solid wooden structure attached to a raft or sledge. It was soon to be used on carts for conveyance of goods and pulleys for lifting objects and further developed as grinding wheels for producing flour from wheat.

Both the above have played a crucial role in the emergence of man and must be woven into a tapestry of life where war and conflict were, perhaps, the most overriding issues of the day and curiosity was in second place to survival.

Without trying to belittle the inventions of fire or the wheel, it is likely that both would have been man copying nature. There would have been many times when cave dwellers would have watched stones cascading down mountains and it would have been obvious that round stones roll with more agility than square ones. Similarly, forests near volcanoes would catch fire and this would lead to the idea that certain materials could be made to ignite and these were just the materials that could be used in fires. Science can be like this but IT CAN BE FAR MORE- it is the ability of mankind to reach out to a virtual world - Newton gazing at the solar system from afar or Einstein riding on a light beam - science is that wonderful link between mind and matter.

Science, or natural philosophy as it is often called, seems to have started a few hundred years BC with names like Archimedes (287 – 212 BC), Aristotle (384 – 322 BC), Pythagoras (570 – 500 BC) Eratosthenes (276 – 194 BC) and Hipparchus (170 – 113 BC) asking questions as to the nature and role of the universe.

To get our first glimpse of science/ Physics ( some would call it mathematics!) we can follow the reasoning that results in every school pupil’s delight, namely, the Pythagoras Theorem.

There is an experimental stage where, perhaps, lengths of wood are placed in a triangular form and the angles at the vertices measured. Every so often a right angle appears and we can make a note of the lengths. For instance, lengths of 3, 4, and 5 will give a right angle; equally 8, 15 and 17 gives a right angled triangle. This experimantal stage presents us with facts , that is, selected groups of three lengths out of all the billions of possible groups give us triangles that contain a right angle.

It would be possible to leave our scientific endeavour after this experimental stage and we would have made a contribution to science. However, for a more complete finishing point a theoretical stage is needed.

It will now be noticed, that by the addition of the red line, the area is composed of squares for the other two sides.( if it is not obvious that two squares are formed then the dimensions of the small coloured square can be used to to calculate dimensions v and w.

-------- v = b + (a-b) = a

-------- w = a - (a-b) = b

(the original position of triangle A is shown in green)

Pythagoras made the startling announcment that:

"The square on the hypotenuse  ( sometimes  lovingly called the hippopotamus) is equal to the sum of the squares on the other two sides."

An equation may now be written in the form    c2  =  b2 +  a2      and, of course, we see that a our  3-4-5 triangle satisfies the Pythagoras Theorem since

 9 + 16 gives 25 

( In algebraec terms, the proof may be directly determined from the composite square, originally drawn on the hypotenuse, given above. This square has area c2 since the hypotenuse has length c. The area can also be determined from the separate objects, namely, one small coloured square (a-b)2  and four triangles with total area 4ab/2, that is 2ab. This gives c2 = 2ab + (a-b)2 which again gives the result above. )

We see here that Nature had yielded up a secret and, in 550 BC or thereabouts, Pythagoras wrote this secret in a concise mathematical form for the benefit of all future generations.

Another great step forward in Physics came from the studies of heavenly bodies.

Mapping celestial objects in the night sky had started mainly in Egypt and by the time that Copernicus started his work in the 1400's many star charts existed with precise data about the characterisitic of stars visible to the naked eye. Though most stars carried out their diurnal rotation in an orderly fashon, there were a few bright objects (planets or wanderers) which had a more irratic movement, the so called retrograde motion.

The above illustration is a modern explanation of this erratic motion in which the celestial object (in this case Mars) normally moves forward in the star field but, for several nights, will move backwards. The stationary points S and S1 indicate times when Mars exactly follows the diurnal motion of the stars and the intervals 1-2, 2-3, 3-4 etc are equal intervals of time.To explain this motion with a geocentic model of the Universe ( SUN MOVING ROUND THE EARTH) was extremely daunting and Nicholas Kopernik, better known as Copernicus, (1473 - 1543) suggested that a heliocentric view of the Universe ( EARTH MOVING ROUND THE SUN ) explained retrograde motion in a simpler manner, as illustrated above. Tycho Brahe (1546 - 1601) carried out more painstaking measurements on the orbits of all the planets and this allowed Johanus Kepler (1571 - 1630) to summarise this observational data into three laws:-

1. Each planet travels in an elliptical orbit with the sun at one focus of the ellipse.

2. If one imagines a line drawn from the sun to the planet, this line sweeps out equal areas in equal periods of time.

3. The distance,d, of the planet from the sun uniquely determines the length of time required by the planet to complete one orbital revolution or period t. A concise statement is given where d3 is proportional to t2.

The arrival of Galileo Galilei (1564 - 1642) onto the scientific scene brought fresh confirmation to a heliocentric model. With observations of Jupiter through a telescope, four moons were seen to be revolving round the planet. So the long held idea that earth was special - created by God - and was at the centre of things in the Universe was probably an illusion. The moons of Jupiter had little regard for Earth being at the centre of all things and were happy to revolve round a different centre, namely, planet Jupiter. Galileo reiterated the heliocentric theory but brought down the wrath of the Church who, in the end, banned him from working on anything concerning motion in the Universe.

Isaac Newton, (1642 - 1727), the father of modern science, now made a momentous leap.

He used all the facts that had been accumulated from astromomical observations (like Pythagoras with his sets of three special numbers) and developed his theory of gravitational attraction.

He showed that planetary motion was caused by the mutual attraction of the planet to the sun by a gravitational force F                                              where                  F = G (Msun mplanet) / d2

                                                   Msun and mplanet are masses of the sun and planet respectively

                                                    d is the separation

                                                     and G is the gravitational constant - ----    6.67 x 10-11 Nm2kg-2

Perhaps we could follow this through a bit further and, for the sake of simplicity, assume the orbits of the planets are circular. Kepler's Laws would now read :  1 the planets travel round the sun in circular orbits with the sun at the centre : 2 Equal areas are swept out in equal times -- this means that the planets have constant speeds : 3 we substitute Newton's gravitational formula into the second of Newton's motional laws ie force=mass x acceleration

                                         G (Msun mplanet) / d2      =   mplanet  x  acceleration

                                          Now acceleration for circular motion is v2 / d

   On substitution we find that the mass of the planet cancels out so v2  = constant / d

    Now the time for a planet to complete an orbit is 2 x PI x d / v and we call this the period t.

So eventually we reach Kepler's third law that    t2   =   constant x   d3 . 

No longer could there be any doubt that the sun was, indeed, at the centre of the solar system and earth was a pretty run of the mill planet.

Later Henry Cavendish (1731-1810) determined the Gravitational constant on earth by measuring the force of attraction between metal spheres. His value commpared well with Newton's values thus showing the universality of Physics - it explains nature on earth or in the vast reaches of the universe .

Newton showed how science was to be carried out - experimental observations ( for this case of planetary observations the experiments covered many centuries) - marshalling facts into an orderly form, these so called laws are a short hand or concise way in which to express accumulated data ( for planetary motion we have Kepler's three laws) - and finally the establishment of a theory to provide an greater understanding of nature.

The scientific method has not changed since Newton's days and it has been accepted as the one true method for studying the Natural world.


There is not space here to cover  all the many and varied aspects of Physics that have developed since the days of Newton but we can be very grateful to Professor Crowell who has put a complete text on the internet.  If you visit the whole evolution of Physics can be studied in depth or you can "dip in and out" for any particular topic. For a more leisurely read I would suggest The Ascent of Man by Jacob Bronowski. It is an almost word for word transcript of the original TV series from the 1970's. Youtube has done a video clip which does say quite a lot about science from the back drop of Auschwitz - any scientist should never play at being God!

Some other sources of Physics textbooks can be given:-

Alonso and Finn have separate books on the following subjects -------1 Mechanics, 2 Interactions and Fields, 3 Waves, 4 Quantum Physics and 5 Statistical Physics. Most of their material is available on-line.

The Motion Mountain series by Christopher Schiller  will keep you very busy!!

It is a truely monumental work- Vol 1 Fall, Flow and Heat (90MB) , Vol 2 Relativity (42 MB), Vol 3 Light, Charges and Brains (56 MB), Vol 4 The Quantum of Change (22 MB) Vol 5 Pleasure, Technology and Stars (70 MB). The is additional Mega Bytes if you wish -- The STRAND at 16 MB. The excitement packed into these volumes is phenonenal == please read on!!!!!!!!!

The following is an exerpt out of the first book on Mechanics

First steps in Physics

Studying physics is an exciting and challenging adventure. To be a professional physicist is even more exciting. Perhaps it is one of the most pleasing activities of the human intellect since, in the authors' opinion, nothing appeals more to the mind than learning about the world we live in and unraveling the secrets of nature.It may seem unnecessary at this point to tell pupils what physics is about, why it is so challenging and interesting, or what its methods are, since he/she already has some familiarity with this science. However, precisely because of one's familiarity with physics, it is desirable to analyze and review the objectives and methods of this science before embarking on its study at a somewhat higher level.

What Is Physics?

The word physics comes from a Greek term meaning nature, and therefore physics should be a science dedicated to the study of ALL natural phenomena. In fact, until early in the nineteenth century physics was understood in this broad sense, and it was called "natural philosophy." However, during the nineteenth century and until very recently, physics was restricted to the study of a more limited group of phenomena, designated by the name of physical phenomena and loosely defined as processes in which the nature of the participating substances does not change (chemistry was concerned with changing substances and biology was concerned with the living world). This somewhat awkward definition of physics has been gradually discarded, returning to the broader and more fundamental concept of previous times. Accordingly, we may say that physics is a science whose objective is to study the components of matter and their mutual interactions. In terms of these interactions the scientist explains the properties of matter in bulk, as well as the other natural phenomena we observe.As you progress through a Physics course, you will witness the way this program is developed from basic and general principles and applied to the understanding of a large variety of physical phenomena, apparently unrelated but obeying the same fundamental laws. Once these great principles are clearly understood you will be able to attack new problems with great economy of thought and effort.

The Classical Branches of Science

Most of our ancestors, having inquiring minds, were curious about how nature worked. At the beginning the only source of information was their senses, and therefore they classified the phenomena they observed accordingly. Light was related to the act of vision and optics was developed as a more or less independent science associated with this act. Sound was related to the act of hearing and acoustics developed as a correlative science. Heat was related to another kind of physical sensation, and for many years the study of heat (called thermodynamics) was yet another autonomous branch of physics. Motion, of course, is the most common of all directly observed phenomena, and the science of motion, mechanics, developed first. Later, thermodynamics and electromagnetism were added to the list and by the end of the nineteenth century most physicists thought that the subject was reaching completion.

The Quantum Branches of Science

It came as something of a surprise that, in the early 1900's, a new era in Physics was just beginning.

In 1900 Max Planck derived the correct energy distribution of radiation from a hot body using a revolutionary assumption of "packets" of light energy. A few years later, in 1905, Einstein showed, that to explain the photoelectric effect, this same concept of "packets" of light energy (or photons) had to be used. The floodgates were now open and the quantum world had arrived.

It is fitting that the story be told by a younger member of the scientific community, my daughter's nephew.

On the Origins of Quantum Mechanics            Lewis Weinberger

"It seems to be one of the mysteries of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power"               P.A.M Dirac [1]


By the end of the 19th Century, many established physicists believed that the physics of the time was almost a complete theory of the universe - all that remained was for them to refine their measurements. Albert Michelson stated in his book, Light Waves and their Uses (1903) [2] "The more important fundamental laws and facts of physical science have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote."

There were a number of loose ends, however, that still needed to be solved. The work of physicists such as Max Planck, Albert Einstein, Niels Bohr and many others led to new discoveries: soon more problems with the 'old' physics of the 19th Century arose. It seemed as though classical physics was unravelling dramatically, and a new theory of strange quantum effects would have to be formulated. Over the next century many brilliant physicists contributed to what is one of the most effective and well-tested theories in physics.

In this essay the theoretical contributions of Werner Heisenberg, Erwin Schrodinger and Paul Dirac will be explored.

Setting the scene (1900- 1924)

In order to understand the reasoning behind Heisenberg, Schrodinger and Dirac's formulations, it is important to consider the events that preceded them.

One of the 'loose ends' of classical physics was black body radiation - the discovery that a black body1 in thermal equilibrium emits electromagnetic radiation. The intensity of this radiation was observed to have a frequency dependence, but theoretical attempts to derive this result were unsuccessful. Then in 1900, Max Planck derived the correct distribution, using a seemingly bizarre assumption that the radiation's energy is quantised [3].

(1 An object that absorbs all electromagnetic radiation, and consequently is a perfect emitter.)

He postulated that a quantised amount of light, called a photon, would have an energy, E, dependent on its frequency f:

                                    E = hf                       where h is a constant referred to as Planck's constant.

Using this result, in 1905 Albert Einstein was able to explain another of the loose ends: the photoelectric effect [4]. When certain frequencies of electromagnetic radiation are incident on metals it can cause the emission of electrons. Einstein realised that these quantised photons were exciting individual conducting electrons in the metal, which explained some of the mysterious aspects of the effect. This useful description of light as a particle conflicted with the previous theories of light as a wave, and led to the problem known as wave-particle duality. It seemed impossible that it could be both a particle and a wave, and yet light was observed to have the properties of both. Then in 1913, Danish physicist Niels Bohr published 3 papers that would truly set the ball rolling for the quantum renaissance of physics. Bohr had spent time in England, working at the Universities in Cambridge and Manchester, with other physicists such as Ernest Rutherford. Inspired by Rutherford's planetary model of the atom, which suggested that electrons orbited the positively charged nucleus of an atom like the planets in the Solar System, Bohr created a model using Planck's quantum hypothesis. In his model the electrons could only take specific orbits at discrete radii, unlike in the previous models where the radii could be as a continuous range of values[5]. He hypothesised that the electrons could jump between radii upon the exchange of energy - here in its quantised form, the photon. This model received a mixed response from the physics community: the accuracy of its predictions was undeniable, but it presented such a strange idea that many would not accept it.

Further important developments were made in the early 1920s. In 1923 French physicist Louis de Broglie published 3 papers on the nature of particles and waves [6]. He suggested that wave-particle duality should extend to matter: that particles such as the electron should also exhibit wave-like properties. The wavelength of this wave would be dependent on the particle's momentum, p, in the following relation:

                        Wavelength   =    h/p

This peculiar idea was later proven in the electron diffraction experiments of 1927 and 19282. It was also a useful way to understand the Bohr Model - the 'electron' waves existed as standing waves in the atom, and each orbit was a different harmonic mode.

These developments were extremely important in the understanding of the quantum nature of reality. However, it was not until later that these effects would be explained by an overarching theoretical framework. Heisenberg's Matrix Mechanics (1925) and the Uncertainty Principle (1927)

"Heisenberg's name will always be associated with his theory of quantum mechanics, published in 1925, when he was only 23.

(2Davisson and Germer (1927), and G.P Thomson (1928))

The article then continues through to the Dirac equation - a good effort.

The Manchester series have always been a great asset to teaching and learning in Physics......

The Manchester Physics Series .General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester, UK.

Properties of Matter B. H. Flowers and E. Mendoza

Optics Second Edition F. G. Smith and J. H. Thomson

Statistical Physics Second Edition F. Mandl

Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow

Solid State Physics Second Edition J. R. Hook and H. E. Hall

Quantum Mechanics F. Mandl

Particle Physics Second Edition B. R. Martin and G. Shaw

The Physics of Stars Second Edition A. C. Phillips

Computing for Scientists R. J. Barlow and A. R. Barnett

Libraries should stock multiple copies of these texts.

Audio Visuals in Physics

What a revolution here!!! In the 1950s/60s the blackboard reigned supreme, perhaps coloured chalk. Slowly other devices crept into the classroom -- notably the Super 8 film loop.

Super 8 mm film is a motion picture film format released in 1965 by Eastman Kodak as an improvement of the older "Double" or "Regular" 8 mm home movie format.

The film is nominally 8 mm wide, exactly the same as the older standard 8 mm film, and also has perforations on only one side. However, the dimensions of the perforations are smaller than those on older 8 mm film, which allowed the exposed area to be made larger. The Super 8 standard also specifically allocates the border opposite the perforations for an oxide stripe upon which sound can be magnetically recorded.

The Open University used audio-visuals extensively and their material is/ was excellent. Now, the sky is literally the limit with YouTube presentations and animations for any subject area - most of the American Universities have free downloadable material.

And what about personalities - do we need, say, Patrick Moore's or Brian Cox's? Undoubtly we need both but my feelings are that most Physics teachers will be closer to the Patrick Moore  end of the scale. Charisms of teachers often lay hidden and I remember at Leeds University being taught VECTORS by a Dr Gandy; I found his presentation hopeless and told him so. Well, he offered me his own time for one or two weeks to catch up and I found him to be a most kindly and considerate person. Only later did I learn that he had been part of Alan Turing's team in Manchester before coming to Leeds.

In conclusion

As the picture on the index page suggests -- whether we look into the skies with telescopes for discoveries of black holes, dark matter .....or deep into the atoms to examine the microscopic world  of quarks Higgs bosons are bound to marvel at the wonders of creation.

Well, in the following pages I wish to engender a passion for science, and Physics in paticular,  so, good luck and good hunting .

Just one last thought - Physicists are concerned about many things and one thing which is uppermost in their minds is the well being of our planet - we would dearly love to leave the world in better shape then we found it. Over these last fifty or so years I have noticed that waste of resources -- energy, food, materials, intellectual and inventive ideas ,-- to mention a few--, are becoming very commonplace. Please read the following passage and try to cut down on waste.

Waste not .... Want not !!!!

Helen Czerski's, article [1] about keeping rust on her bike at bay was so dear to my heart as I, too, pedal my way around the roads and countryside. And, like Helen, I severely neglect my long suffering work horse.

The subject matter of Helen's article comes under a much wider umbrella of "waste and decay" and perhaps I can reinforce her story with a personal example.

My toaster packed up recently and, as Murphy's Law is ever present, it was out of guarantee. By holding down the activation lever I discovered that all the elements were functioning normally but the lever just sprung up on removal of my hand ( there is a spring mechanism which "pops up" the toast ) . Whereas the old toasters used bi-metallic contacts to time the toasting period, the newer toasters use an electromagnet which holds a "keeper" down. Current is then passed through the electromagnet for a given time set by an electronic timing circuit. A view of the electromagnet is given in Fig 1.

Figure 1 An electromagnet -"keeper" system to enable the toasting period to be set

Investigations showed that a bread crumb had become trapped between the poles of the electromagnet and the keeper so that, no matter how hard the lever was pressed down, there was an appreciable gap between the two. A little modelling, Fig. 2, showed that the Magnetic Field, which holds the keeper down against the "pop up" force, is much reduced if a gap is present.

Figure 2 Magnetic Field diagrams with magnet to keeper distance varied - for simplicity a two pole magnet is presented here (produced with the QuickField simulation package).

The force, F, on the keeper is given by:-

(1)     F = (A B2 )/(2 u0)

where B is an average Field in the gap between the keeper and the electromagnet.

A is the area of contact between the keeper and the electromagnet

and µ0 is the permeability of free space.

As equation 1 shows, the force is proportional to the square of the magnetic field and a reduction of this attractive force means that it does not match the "pop up" force. The heater elements are therefore only energized for a fleeting instance as one presses down the activation lever.

The remedy was simple the gap area was scraped clean of bread crumbs and the toaster is now working.

Now, what would have happened to the toaster if such a simple solution had not presented itself ? Cannibalise the item for spares or an immediate dispatch to the bin?

A few years ago [2] I advocated that the three "R's" that I was brought up with : reading, (w)riting and (a)rithmetic should be taught in schools as Reduce, Re-use and Recycle. But I now find I have to add another "R" to the three "R's"; this time R is for Repair but how common is this word in today's world? Dindarian at al [3] have recently used the microwave cooker as a case study for the concept of "return of product and reuse opportunities" and I could add to this one item an everlasting list: cars, 'fridge mountains, a wake of washing machines, cookers, toaster .... the list is endless before we start on media and computing/ communication items. Either obsolescence or the malfunction of one small component will often render a product useless and then the whole product must be binned!

We all know that Mother Nature has given us a different story - decay is present in nature, yes, but a whole eco system has been set in place to make sure that there is no waste. A magnificent edifice like a tree will eventually decay but nature makes sure it will decay into useable products.

Perhaps the TV presenter John Humphrys should have the last word with the following excerpt which is taken from The Sunday Times, 9th April 2000.

"Now, if you will excuse me, I need to pop outside because a police horse has just deposited a great pile of manure in the road in front of my house. It will do wonders for my vegetables and it would be a shame to leave it there to be squashed by a passing car. However, I shall cover my head with a balaclava just in case anybody sees me with a shovel. They would think I was crazy."

(The full article, entitled "Waste not - want not" is used as a comprehension exercise for the GCSE examination board, Wales ) .

The text "Long Emergency" by Kunstler [4] expresses similar sentiments to John and he gives dire warnings that, without any change in our present lifestyle, humankind may be beset by formidable problems in the latter part of the twenty first century .


[1] H. Czerski (2015), "Everyday Science" BBC Focus magazine, Issue 276, 33.

[2] F.Thompson, (2009), "The three "R's" make a comeback, Physics Education, Vol.43, 324.

[3] A. Dindarian, A. A. P. Gibson and J. Frota-Neto (2012) "Product returns and Potential reuse opportunities" J. of Cleaner Production, Vol, 32, 22.

[4] J. H. Kunstler " The Long Emergency" Grove/Atlantic, 2005.

                                                                                    top of page