Top 10 Important Equations In Physics

These simple-looking equations went on to have great consequences and applications in science, society and technology. Let us take a look at the ten most influential formulae in physics (in no particular order) which have changed the course of history.

Second law of motion

The force, often intuitively described as push or pull, is actually the cause of acceleration in a moving particle. Without it coming from any external agency, the particle cannot undergo change in the way it goes. Newton defined the force formally in 1686 in the famous equation, F=ma.

It tells you how powerful an engine has to be in order to pull a car, how much thrust required to lift a rocket, how far a cannonball flies and so on. But more importantly, the equation helped debunk the Aristotelian beliefs which had remained unchallenged for thousands of years.

According to Aristotle, force is necessary to keep an object going. Why otherwise would a ball rolling on the ground eventually stop? Because, Aristotle said, it isn't pushed anymore, that's why.

Then, in the 17th century, Italian scientist Galileo Galilei explained, with experiment, "The ball stopped due to the ground being rough and had it been sufficiently smooth, the ball would roll forever. No force required!"

Newton said further, that the state of rest or uniform linear motion both imply zero acceleration. Thus, the particle will remain in place or keep going at the same rate and it will maintain itself in the state in which it's been until of course when acted upon by external force.

Energy-mass relation

It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing. The mass of a body is a measure of its energy content. If 1 gram of mass is converted into energy, it'd be 90 trillion Joules. This is equal to the energy emitted by a 100 watt light bulb for 30,000 years!

It is important to understand that Einstein's most famous equation is not his major work. The formula is just so well-known because of its association with the atomic bomb. Einstein himself had said, "If I had foreseen Hiroshima and Nagasaki, I would have torn up my formula in 1905," despite him having played a minor role in the Manhattan Project.

Uncertainty principle

Formulated by Werner Heisenberg in 1927, uncertainty principle is one of the cornerstones of quantum mechanics. The equation single-handedly ended the classical determinism, meaning, that in the realm of infinitesimal atoms, chance has its play and the drama of existence is not absolutely predestined in character.

In its most familiar form, it says that the more precise the measurement of position, the more imprecise the measurement of momentum, and vice-versa. Thus, one can never know with perfect accuracy both of those two important factors which determine the movement of one of the smallest particles, its position and its velocity, at the same instant.

The uncertainty principle was immediately rejected by leading physicists of the time, including Albert Einstein. There, Niels Bohr did try his best to convince Einstein that the uncertainty relation is fundamental law in physics. Einstein still refused, and they agreed to disagree. By 1933, the political situation became much worse in Germany, and Einstein moved to the United States.

In 1954, Heisenberg visited Einstein's house in Princeton. They talked only about physics, but Einstein's position on the principle hadn't changed. In 1955, Einstein passed away leaving Werner Heisenberg disheartened that he had failed to get Einstein's endorsement of his uncertainty relation.


Although Einstein and others objected to Heisenberg's and Bohr's views, even Einstein had to admit that they were indeed a logical consequence of quantum mechanics. But for Einstein, something still was missing and the quantum mechanics was incomplete, "I am convinced that god does not throw dice," he claimed metaphorically.

Heisenberg, supported by Bohr, Pauli, Schrödinger and others, maintained until his death that quantum uncertainty is not inaccuracy of the measurement, it is inherent in quantum phenomena. It leads to probabilistic and not deterministic outcomes.

Maxwell-Faraday equation

In 1831, as the story is usually told, the prime minister or some other senior politician was given a demonstration of electromagnetic induction by Faraday. When asked, “What good is it?” Faraday replied: “What good is a newborn baby?” Fifty years passed before electric power really took off as envisioned by Faraday.

Generators and motors both make use of Faraday's Law. The equation by Maxwell became the foundation of power generation hence making Faraday the father of electricity. Maxwell said of Faraday, "He is, and must always remain, the father of that enlarged science of electromagnetism."

Dirac equation

Symmetry is the keyword of physics and Dirac used it perfectly in 1928. He developed an equation that explained spin number as a consequence of the union of quantum mechanics and special relativity. The equation also predicted the existence of anti-matter, previously unsuspected and unobserved, and which was experimentally discovered in 1932.

This accomplishment has been described on par with the works of Newton, Maxwell, and Einstein before him. Dirac even speculated that there may also be mirror universe of anti-particles, thus becoming a source of inspiration for science-fiction writers. Dirac was also equally famous for his contribution to quantum electrodynamics, which described how electric and magnetic forces would work on the scale of things smaller than atoms.

Law of entropy

The famous inequality which says that when energy changes from one form to another form, or when matter moves freely, the disorder in a closed system increases. According to renowned astronomer Arthur Eddington, "The law that entropy always increases, holds, I think, the supreme position among the laws of nature."

The concept of the second law of thermodynamics applies not only to internal combustion engines used in our cars, motorcycles, ships and airplanes but also to explain the processes of life, when considered in terms of cyclic processes.

The second law also has profound consequences for the universe in large scale. Imagine being shown a video clip of a cup being dropped and breaking. You'd clearly be able to tell whether the video was being played backward or forward, from the flow of entropy.

Similarly, if the movie of our universe is played backwards, the universe would be getting more and more ordered, like the cup, and when played forward, we'd expect it getting disordered, like the pieces of broken cup.

Einstein field equations

Einstein's equations led to the fusion of the three dimensions of space and the one dimension of time into a single four-dimensional spacetime. The expression on the left hand side of the equation represents the curvature of spacetime. The expression on the right is the energy density of spacetime. The equation dictates how energy determines the curvature of space and time.

The cosmological constant term (Λ) was introduced by Einstein to allow for a universe that is not expanding or contracting. This effort was unsuccessful because in 1929, astronomer Edwin Hubble discovered evidences for an expanding universe. Einstein was invited by Hubble to see for himself that the universe indeed was changing.

As a result, Einstein abandoned the cosmological constant in the equation, calling it the biggest blunder he ever made. So from the 1930s until the late 1990s, most physicists assumed the cosmological constant to be equal to zero. But, recently improved astronomy techniques have found that the expansion of the universe is accelerating implying the non-zero value of the constant.


Why are the Einstein field equations important in physics? Firstly, because they unify the two concepts of space and time, previously considered separate by the limitations of our intuition, into one spacetime. Just like Maxwell had unified electricity and magnetism into electromagnetism in the 19th century.

Secondly, they describe – not the force – but the fundamental "interaction" of gravitation as a result of spacetime being curved by energy (mass too is energy from Einstein's energy-mass equivalence).

Although Newton did give the formula to calculate the magnitude of gravitational force between any two bodies of mass separated by a distance, he didn't quite explain the cause of gravitation in the first place.

Wave equation

The single-dimensional wave equation has a scalar function (u) of one space variable and one time variable since waves propagate in space, and in time also. This equation was first written by French mathematician Jean le Rond d'Alembert, hence it's sometimes also called the d'Alembert's equation. Swiss mathematician and physicist Leonhard Euler wrote it in three dimensions in 1707.

We are constantly surrounded by waves, whether perceptible to us or not, they are always there. Like when you play a guitar or drop a stone into a pond. The wave equation isn't as elegant as others on this list but it is groundbreaking as it's been applied to sound waves (and instruments), waves in fluids, waves in earthquakes, light waves, quantum mechanics and general relativity.

Planck's equation

This formula is responsible for the birth of quantum mechanics, also television and solar cells. Leading German physicist of the time Max Planck postulated in 1900, that energy was quantised and could be emitted or absorbed only in integral multiples of a small unit, which he called "energy quantum".

Einstein extended Planck's idea in 1905 when he introduced the concept of "light quantum", the particle of light, or photon. Thus, the electromagnetic radiation wasn't continuous like a wave but isolated in the packets of light, Einstein proposed.

Planck had simply introduced the equation as a trick to solve a problem with black body radiation, but Einstein envisioned it to be more. In 1887, experimenter Heinrich Hertz stumbled upon the photoelectric effect for the first time; the emission of electrons when light of specific frequency hit a material.


The phenomenon of photoelectric effect remained largely unexplained, even with the wave theory of light, until the arrival of Planck-Einstein relation in 1905. Einstein described it in terms of particle-particle interaction between the photon and electron. He said, "...below some critical frequency, no photon has enough energy to knock an electron free."

This means that if a photosensitive material requires photons of blue light to emit the electrons, which is the characteristic of the material, then the photons of green or yellow light won't be able to knock the electrons out of the material.

The characteristic energy or work-function of the material is absorbed, to loosen the bonds, and then the remainder of the energy is observed as kinetic energy of the free electron. Einstein's clarification was consistent with the law of conservation of energy. He was recognized with Nobel Prize in physics for his explanation of the photoelectric effect (and not for energy-mass relation or relativity).

Planck said his introduction of "quantum" in 1900 was an act of desperation but when Einstein adopted it and gave it meaning, a whole new debate had started and the old laws were swept away within a decade or so. Einstein who himself was accountable for it refused to endorse the new quantum revolution.

The discovery by Planck and Einstein became the basis of all twentieth-century physics, without which, it would not have been possible to establish a workable theory of molecules and atoms and the energy processes that govern their transformations.

Schrödinger's equation

In his 1924 doctoral thesis, French physicist Louis de Broglie proposed, that just like light has both wave and particle properties, electrons must also possess wave-like properties, in order to support the energy-matter symmetry. Two years later, in 1926, Austrian scientist Erwin Schrödinger published an equation, describing how the matter wave should evolve in space and in time.

Just like Newton's equations are used to calculate how a football behaves when kicked, you use the Schrödinger's equation to calculate the behaviour of electron in the orbit of an atom. More generally, it is used for many calculations in quantum mechanics and is also fundamental to much of the modern technology, from lasers to transistors, and the future development of quantum computers.

Self-taught scientist who became father of electricity

Although Faraday received little formal education, he was one of the most influential scientists in history becoming the inspiration for likes of Einstein and Tesla. He is best known for the discovery of electromagnetic induction, his invention of the electric motor, contributions to electrochemistry or due to the fact that he was responsible for introducing the concept of field in physics.

In 1873, the standard unit of electrical capacitance was named farad in his honor. The Bank of England unveiled a £20 bill with his portrait in 1991 as he joined a distinguished group of Britons with their own notes, including William Shakespeare, Florence Nightingale and Isaac Newton. Many claim him the father of electricity and in fact, Maxwell himself had said, "Faraday is, and must always remain, the father of that enlarged science of electromagnetism."

Early education

Michael Faraday was born to Margaret and James Faraday on 22nd September, 1791. The family was not well off so they moved to London seeking more opportunities. The young Faraday, who was the third of four children, having only the most basic school education, had to educate himself, while working on the streets of London.

At the age of 14, Faraday became an apprentice to a local bookbinder and bookseller, George Riebau, in Blandford Street, Marylebone. During his seven years of apprenticeship, Faraday made good use of the priceless access to books which his employment gave him and which his generous employer allowed.

Faraday was deeply motivated by the book, "Conversations on chemistry" by Jane Marcet so much so that when 20 years old, he attended the lectures by the most renowned English chemist of the time, Sir Humphry Davy. Faraday later on sent Davy a 300-page book based on the notes that he had taken during these lectures. Davy's reply was immediate, kind, and favourable.

The first invention

In 1813, when Davy damaged his eyesight in an accident with nitrogen trichloride, he decided to take Faraday as temporary assistant. In the class-based English society, Faraday was not considered a gentleman, because of which, Davy's wife declined to treat Faraday as an equal making his life so miserable that he contemplated suicide.

But Davy refused to let the talented young man go. He employed Faraday permanently as his scientific assistant much to his wife's displeasure. They went together on a tour of the continent meeting the scientific elite of Europe as well as exchanging ideas with them. Davy joked that his assistant Michael Faraday was his greatest discovery; little did he know that he'd be right!

In 1820, Danish physicist Hans Ørsted discovered (although by accident) that electric current in a wire could deflect magnetic needle in the immediate vicinity. Davy wasn't bothered the least by it, but Faraday, on the contrary, declared it one of the greatest discoveries of mankind. One year later, Faraday invented the electric motor by using the same principle, which is today the basis of fans, pumps, compressors, elevators, and refrigerators.

Faraday's rapid rise made Davy jealous and he became indifferent to him, treating him more as a challenger. Towards the end, Davy even accused Faraday of plagiarism causing Faraday to cease all research in electromagnetism until his mentor's death. In 1829, Davy was paralyzed by a stroke and passed away aged 50. Despite the bitter ending, Faraday described Davy fatherlike, kind and protective.

Electromagnetism

Thus, Faraday began his great series of experiments, in which he discovered the law of electromagnetic induction. The breakthrough came when he wrapped two insulated coils of wire around an iron ring, and found that upon passing a current through one coil, a brief current was induced in the other coil.

Faraday went on to invent a rudimentary generator in 1831 and as the story is usually told, the prime minister or some other senior politician was given a demonstration of induction by Faraday. When asked, “What good is it?” Faraday replied: “What good is a newborn baby?” Fifty years passed before electric power really took off as envisioned by Faraday.

Faraday was little interested in mathematics and his own scientific career was characterized by simple ideas and simple experiments. But the discovery of induction was eventually formalized by Scottish physicist and mathematician James Clerk Maxwell into an equation now known as Maxwell–Faraday equation.

Faraday wrote in a letter to Maxwell, "I was at first almost frightened when I saw such mathematical force made to bear upon the subject, and then wondered to see that the subject stood it so well." The equation by Maxwell became the foundation of power generation hence making Faraday the father of electricity.

Later life

After induction, Faraday formulated the laws of electrolysis in 1834 whose applications are far and wide such as production of industrial chemicals and electroplating. For his unprecedented work, Faraday was appointed the Professor of Chemistry at the Royal Institution without a degree. He was also offered a knighthood but he turned it down citing religion.

In 1836, he invented the Faraday cage, an enclosure used to block the electromagnetic field. You can find a real-life version of Faraday cage right inside your kitchen: the metal shell in the microwave oven acts like a Faraday cage as it prevents the microwaves inside the oven from leaking out. Faraday cages are also used in MRI scans to prevent external frequencies from causing any distortion to the data coming from the patient.

Beyond his scientific research into areas such as chemistry and physics, Faraday accepted numerous, and often time-consuming, service projects for the greater good of the country. For example, every Christmas, Faraday would give free science lectures to a general audience, including young people, in an informative and entertaining manner.

He delighted in filling soap bubbles with various gasses in front of his audiences and marveled at the rich colors of polarized lights, but the lectures were also deeply philosophical. In this way, Faraday was really the world's first science communicator. He delivered a total of nineteen such lectures until he was 53 years old.

Many years after his scientific career, Faraday dedicated a book to George Riebau, his first employer, writing: "...you kindly interested yourself in the progress I made in the knowledge of facts relating to the different theories in existence, readily permitting me to examine those books in your possession that were in any way related to the subjects occupying my attention."

Science and religion

Faraday was a devout Christian although there may have been some conflict between his religious beliefs and his activities as a scientist. Many of his colleagues and especially Henry Bence Jones had claimed through letters and writings that Faraday was a scientist first and religious second, but he was also both.

Jones, who was Faraday's junior, published the book, "The Life and Letters of Faraday", in 1870. Faraday said of himself, "Without experiment, I am nothing. In early life I was a very lively, imaginative person, who could believe in the Arabian Nights as easily as in the Encyclopedia, but facts became more important to me, and saved me. I could trust a fact. One thing is fortunate, which is, that whatever our opinions, they do not alter nor derange the facts of nature."

Faraday's laboratory journal entry on 19 March, 1849 says, "ALL THIS IS A DREAM. Still examine it by experiments. Nothing is too wonderful to be true, if it be consistent with the laws of nature; and in such things as these, experiment is the best test of such consistency." Faraday viewed his discoveries of nature's laws as part of the continual process of reading the book of nature.

When asked about his speculations on life beyond death, Faraday replied, "Speculations? I have none. I am resting on certainties. I know whom I have believed and am persuaded that he is able to keep that which I have committed unto him against that day."

Tagore and Einstein Discuss Physics and Philosophy

Rabindranath Tagore was an Indian polymath who became the first non-European to win the Nobel Prize in Literature for his profoundly sensitive, fresh and beautiful work, Gitanjali, in 1913.

He is also well known to have written the national anthems of Bangladesh and India as well as gave music to the national anthem of Sri Lanka. As a result, his influence, especially in the sub-continent, is going to live forever.

Similarly, Albert Einstein too received the most coveted prize in the year 1921 mainly for his explanation of the photoelectric effect. But he has become more famous for his theories of relativity and for the equation E=mc² meaning the equivalence of mass and energy. Einstein was not just a great scientist but also a man deeply involved in the matters of society and politics.

The two gentlemen decided to meet on July 14 (1930) in Berlin at Einstein’s place to talk about variety of things, ranging from the nature of reality to their individual tastes in music. Tagore in fact suggested that their conversation be recorded and put together in a book.

However, when they met, Tagore did not know sufficient German and Einstein’s English was too weak to converse with. Hence they had to bring interpreters for the meeting. Neither Tagore nor Einstein was happy with the recorded conversation as the translations had lost their charm. Therefore, they themselves corrected their own parts before making it public. The book was published titled, Science and the Indian tradition.

On truth and beauty

Einstein: Are truth and beauty independent of man?

Tagore: No.

Einstein: If there would be no human beings any more, would the Apollo of Belvedere no longer be beautiful?

Tagore: No.

Einstein: I agree with regard to this conception of beauty but not with regard to truth.

Tagore: Why not? Truth is realized only through man.

Einstein: I cannot prove if my conception is right but that is how I see it.

Tagore: We individuals approach truth through our own mistakes and blunders, through our accumulated experiences, through our illumined consciousness – how, otherwise, can we know the truth?

Einstein: I know not how to prove scientifically that truth must be conceived as truth and be independent of humanity; but I believe it firmly. I believe, for instance, that the Pythagorean theorem in geometry is independent of the existence of man. If there is a reality independent of man, I believe, there is also a truth relative to this reality.

Tagore: But truth must essentially be human otherwise whatever we individuals realize as true can never be called truth, at least the truth which is described as scientific and which only can be reached through the process of logic, in other words, by an organ of thoughts, which is human. The nature of truth which we are discussing is an appearance, that is to say, an illusion.

Einstein: The question is whether truth is independent of our consciousness. According to your conception, which may be the Indian conception, truth is not the illusion of the individual, but of humanity as a whole.

Tagore: What we call truth lies in the rational harmony between the subjective and objective aspects of reality, both of which belong to the personality of man. In any case, if there be any truth absolutely unrelated to humanity, then for us it is absolutely non-existing.

Einstein: Then I'm more religious than you are!

Tagore: I believe more in the universal human spirit, in my own individual being. I never believed in any religious institution and practices whether it was Hinduism or Islam or Christianity. My religion is realized through the divinity of humanity and the humanity of god.

On duality

Tagore: I have been told that in the realm of infinitesimal atoms, chance has its play; the drama of existence is not absolutely predestined in character.

Einstein: The facts that make science tend toward this view do not say goodbye to causality. In the macro-world, there is order as well as predictability. However, in the minute world, like you said, the order is not perceptible.

Tagore: I find a parallel in human psychology. Our passions and desires are unruly but our character subdues these elements into a harmonious whole. Does something similar to this happen in the physical world? Are the particles rebellious and dynamic with individual impulses? And is there a principle in the bigger world which dominates them and puts them into an orderly organization?

Einstein: Even the particles are not without statistical order; atoms of radium will always maintain their specific order, now and ever onward, just as they have done all along. There is, therefore, a statistical order in the particles.

Tagore: That is beautiful. It is the constant harmony of chance and determination which makes nature eternally new and living.

Einstein: I believe that whatever we do or live for has its causality; it is good, however, that we cannot see through to it.

On music

Einstein: How’s the Indian music different from that in the west?

Tagore: The musical system in India is not so rigidly fixed as is the western music. We praise the composer for his genius in creating a foundation, but we expect from the player his own skill in the creation of variations of melodic flourish and ornamentation.

Einstein: That is only possible where there is a strong artistic tradition in music to guide the people’s mind. In Europe, music has come too far away from popular art and feeling and has become something like a secret art with conventions and traditions of its own.

Tagore: So you have to be absolutely obedient to this too complicated music.

Einstein: Can the Indian music be sung without words? Can one understand a song without words?

Tagore: Yes, we have songs with unmeaning words, sounds which just help to act as carriers of the notes. In India, the measure of a singer’s freedom is in his own creative personality. The singer is at liberty to add his own words to the song which he is singing.

Einstein: It requires a very high standard of art fully to realize the great idea in the original music, so that one can make variations upon it. In our country the variations are often prescribed. It seems that your music is much richer in structure than ours. Japanese music also seems to be so.

Tagore: I am deeply moved by the western music and I feel that it is great, that it is vast in its structure, and grand in its composition. Our own music touches me more deeply by its fundamental lyrical appeal. European music is epic in character; it has a broad background and is Gothic in its structure.

Einstein: Yes, yes, that is very true. When did you first hear European music?

Tagore: At seventeen, when I first came to Europe. I came to know it intimately, but even before that time I had heard European music in our own household. I had heard the music of Chopin and others at an early age.

What Are 7 Qualities of A Great Physics Teacher?

Educational rockstar

All the excellent physics teachers are great communicators who draw the attention of their students without fail. Why, because they are witty, humorous and confident when they teach physics. Take Professor Walter Lewin, for example, whose videos have received more than 50 million views on YouTube, collectively.

Real world examples

There are innumerable teachers who merely repeat what's in the textbook and then there are few, who make physics fun and accessible through analogies plucked from daily life.

Paul G. Hewitt has a unique approach to teaching physics that focuses on the ideas rather than the often daunting mathematics. He has believed that with a strong conceptual foundation, students are better equipped to understand the equations and formulas later.

Passion for it

A good physics teacher has not only deep knowledge about the subject but also desire to pass it on to others. Richard Feynman had once said, "I find that teaching and the students keep life going, and I would never accept any position in which somebody has invented a happy situation for me where I don't have to teach. Never!"

To this day, Feynman is mostly remembered not because he was a great scientist but because he was an extraordinary teacher who became guide for his students in time of trouble. He used to say, "teach them to doubt, to think, to question, to make mistakes, to learn from their mistakes and most importantly, to have fun in their learning."

Adaptable

All the good physics teachers listen well, focus on collaboration with their students and adapt to new teaching methods. Sal(man) Khan from Khan Academy is an example who's determined to teach by using technology. Also, Professors Walter Lewin and Gilbert Strang from MIT have adjusted well even in old age.

Gilbert Strang

Approachability

Every good physics teacher is friendly and approachable. Furthermore, he/she is not afraid of doubts, problems and/or feedback from their students. In fact, the good teacher is forever ready to struggle with questions, also taking their students as partners! Walter Lewin, for example, used to accept questions on Quora. Now, he is more available on YouTube and replies to questions in comments. He is 85 years old.

Candle in the dark

In early 1980, H.C. Verma joined the Patna Science College as a lecturer. He found that the students were uninterested in physics because it was too difficult. Also, there weren't any textbooks available in the Indian market which were even remotely relatable.

Thus, a young Professor Verma set about to solve the problem of his students. Ten years later, in 1992, a new book by the name, 'concepts of physics' was published and it became an instant favorite in India. To this day, the book is being used by many science and engineering aspirants. Professor Verma became and burned like candle, illuminating the darkened lives of incurious physics students.

Self development

A bad physics teacher will often beat around the bush in order to hide the fact that he/she does not know. On the other hand, all the good physics teachers accept that they don't know and/or that they're wrong, and moreover, they want to continue to learn. 

10 Examples of Physics From Everyday Life

Not every student will grow up and study physics on a deeper level, but physics extends well into our daily life, describing the motion, forces and energy of ordinary experience. Therefore, it should be possible to illustrate to anyone the physics of everyday life, with examples of course.

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Image formation

Have you noticed that when standing inside a room at night, you can often see your reflection in a pane of glass? In similar way, because there is much less light coming from the bottom of a lake, the surface of the lake will act like a mirror.

But an image can also be formed by refraction. A fish seen in the water will usually appear to be at a different depth than it actually is, due to the refraction of light rays as they travel from the water into the air.

Lastly, there exist phenomena which appear due to combination of reflection and refraction. For example, a rainbow is seen when light passes through water droplets hanging in the atmosphere. The light bends, or refracts, as it enters the droplet, and then reflects off the inside of the raindrop.

Washing machine

The dryer of washing machine is a rapidly rotating container that applies centrifugal force to its contents. The centrifugal force acts in a direction away from the centre and hence can be used to throw the water molecules on the clothes radially outwards during the spin cycle of the washing machine.


Static electricity

When two objects that are not good electrical conductors are rubbed together, electrons from one of the objects rub off onto the other.

The more rubbing between two objects, the more static electricity build up and the larger the electrical charge.


Road safety

When brakes are applied to a moving car, the car and lower portions of the passengers attached to the car come to immediate stop, but their upper portions fall forwards, because of inertia. This is why seat belts as well as air bags are installed in the car.

Roller coaster

The first hill of the ride is always the highest one so that the car collects enough energy to go through all the elevations. As the car goes down, its potential energy decreases but kinetic energy increases. If added together at any part of the ride, the kinetic and potential energies of the car will equal the potential energy that the car had on the first hill.


Spinning

When the figure skater draws her arms and a leg inward, she reduces her moment of inertia thus rotating at a faster angular speed. This is due to conservation of angular momentum.

Handle of the door

If you apply force close to the hinge of the door, the door will not open as it will not be able to rotate about the hinge. But, when you apply the same force farther away from the hinge, the torque will be larger. Hence, the door opens easily with less effort.

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Falling down

Suppose you are climbing a tree, and suddenly you slip and fall down from the tree. Then, you may break a bone or two. But if same thing happens to a little ant, that is, if it falls down from height, it does not get hurt. Why is it so?

From ant’s point of view, the atmosphere is thick and viscous and its experience of falling from a height is similar to ours when we fall through water to the bottom of the pool. The air underneath the falling ant becomes like a large cushion of safety.


Roundness

Nobel prize winning physicist Richard Feynman explains why little drops of water are round in the following video.



Sound game

When a water bottle fills up, the air column or amount of air inside the bottle decreases. As a result, the pitch (or shrillness) of the sound will increase, as it is inversely proportional to the length of vibrating air column. Therefore, you can tell exactly when the bottle is full without even looking.

Summing up

It is hard to imagine of life without physics. Even though one may not be equipped with the kind of mathematics required to fully understand these physical phenomena, one can surely appreciate the fact that they are there. Lots of other examples are available and you just need the eye to recognize them.

Dirac, a fusion of genius and madness, according to Einstein

Paul Dirac, one of the most famous scientists of the 20th century, was a very quiet man. So much so, that his colleagues at Cambridge jokingly defined a unit of speech called "dirac", which meant one word per hour!

But whenever he did speak, Dirac used to extend his abstract thinking to interpret the world literally. This inevitably led him to being an anecdote generator throughout his life and many stories about him abound.

Why do you dance?

In 1929, Dirac and Heisenberg were on board a ship to Japan for attending annual science conference. Werner Heisenberg who happened to be quite a ladies man, used to dance with the young girls on the ship before dinners, while Dirac used to sit watching.

One such evening, Dirac asked, "Heisenberg, why do you dance?"

"When there are nice girls, dancing with them is a pleasure," Heisenberg replied.

Dirac pondered this notion for a while, then blurted out: "But, how do you know beforehand that the girls are nice?"

Heisenberg burst out with laughter.

Physics versus poetry

Dirac and Oppenheimer spent some time together in Göttingen. The two young physicists from different parts of the world had become good friends. In one of these days, Dirac noticed that Oppenheimer wrote poetry.

Dirac asserted, "Robert, I do not understand how a man can work on the frontiers of physics and write poetry at the same time."

"Why not?" Oppenheimer asked.

"In physics, you want to tell something that nobody knew before, in words which everyone can understand. In poetry, however, you go on to describe something that everybody knows about, in incomprehensible ways."

Oppenheimer was left too confused to respond to that.

Dirac went on to say, "The two are incompatible!"

His comments would strike people as odd at first but they would quickly realize that Dirac made perfect logical sense.

Finish this sentence

Once, Dirac and Bohr were seated in the same room. Niels Bohr, known for being a perfectionist, was writing a scientific paper while mumbling at the same time as was his habit.

After some time, Bohr became really frustrated and stopped. He complained, “I do not know how to finish this damn sentence!”

Dirac retorted, "I was taught at school, never to start a sentence without knowing the end of it."

Dirac said something so profound, with such a straight face, that Bohr went on to comment, "Dirac was the strangest man who ever visited my institute!"

I have an equation

American physicist, Richard Feynman, born in 1918, grew up idolizing Dirac. About 40 years later, they met in Poland at a conference. Richard Feynman, by then a theoretical physicist himself, was building upon Dirac's great work.

Feynman, the chatty one, spoke at length, as he wanted to describe new ideas to his hero. Dirac, perhaps intimidated by Feynman's over-enthusiasm, remained quiet all along.

Feynman started to see that it was extremely difficult to get anything out of Dirac. But then, after a long silence, Dirac says, "I have an equation. Do you have one too?"

Dirac also went on to explain as to why he spoke so little, “There are always more people willing to speak than there are to listen.”


That wasn't a question

In 1932, Dirac was appointed the Lucasian Professor of Mathematics at the University of Cambridge. During one lecture in class, a student raised his hand and said, "I don't understand the equation on the top-right-hand corner of the blackboard."

Dirac simply nodded his head in agreement and continued unabated. When asked again, he expressed puzzlement because he thought the student had simply uttered a fact and not asked a question.


Summing up

Paul Dirac knew not when to say what. He remained merry in his own company but suffered agonies if forced into any kind of socializing or small talk.

His colleagues  in Cambridge described him as a “lean, meek, shy young fellow who goes slyly along the streets, walks quite close to the walls, like a thief, and is not at all healthy.”


Albert Einstein once commented on Dirac: "I have a lot of trouble with Dirac. This balancing on the dizzying path between genius and madness is awful!"

Dirac quantised the gravitational field, formulated the most logically perfect presentation of quantum mechanics and predicted the existence of anti-matter. At the same time, he was also equally famous for his strange, unapologetic behavior.