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The Beginning of Physics: Newton’s work

(Last Updated On: December 30, 2019)


In this article we will once again dive in the work of Sir Isaac Newton. I already wrote an article about this one (The Beginning of Physics: Newton) but, he does deserve something more. This time we’ll explore his work in more detail than his life.

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Sir Isaac Newton

This is the eleventh article in the Beginning of Physics series. If you didn’t read the previous part you should definitely do so, specially because Newton’s life is in there:

So where do we start? Good question, and the answer is optics (because I want so)

Newton on Optics

In 1666 Newton discovered some important stuff about light. Like its nature and composition, you know, basic stuff.

This year, as previously said in the last article, was his miraculus year, where he wrote his theory of light and colors.

He observed that when light passes through a prism, different colors are refracted in different angles. This lead Newton to the conclusion that color is a property intrinsic to light itself. This might not seem such a huge deal today (because it’s obvious), but back then this was a serious debate, and Newton ended it!

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He also showed that colored-light doesn’t change its properties. At all. Try it yourself: You may reflect it, scatter it or even transmit it. The light remains the same color. From this Newton came to the brilliant conclusion that color is a result of objects interacting with already-colored-light, rather than being generated by the object themselves. And this is true!!

It should be pretty obvious be now that Newton believed that light was a particle. In fact, people who later believed light was a particle showed Newton’s theories as a proof. This caused a lot of debate on Newton’s theories (like Robert Hooke) but also caused Newton’s entrance on the Royal Academy in 1672.

Newton on Math

Newton’s work has been said to “distinctly advance every branch of mathematics then studied“. His most known work is calculus. Yes, the stuff which is being way too hard for you to learn.

Newton wrote some brief stuff on calculus in 1666 and later worked it hard while on planetary motion (more on that later). He used integrals and derivatives to calculate the motion of planets (because these can be described by the change in velocity, acceleration and other properties).

But now comes the big Revelation: Newton wasn’t the first one to use calculus. I know right, didn’t expect this one… Newton’s Rival was Gotfried Wilbelm Leibniz, born in Leipzig, former Holy Roman Empire, in 1646. He, kind of like Newton, worked basically in every branch of science. Inventor of the two wheeled mechanical calculator, the binary notation (later used on computers) and a major figure in philosophy, Leibniz was quite a badass as well.

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Gotfried Wilbelm Leibniz

Gotfried worked out elements of calculus as far back as 1675, a decade before Newton’s Principia. In this year, Leibniz did what no human being had ever done before: he calculated the area under the graph of a function using integrals! You might not think this is something amazingly awesome, but it really is.

While in is work on calculus, Leibniz made up the symbols of differentials (δ) and the integral symbol, summa (). We still use this symbols, because we use Leibniz system of calculus, not Newton’s! You also didn’t know this one, did you?

So, why is this dispute still a thing really? Because Leibniz would only publish his full version in 1693 in the “Fundamental Theorem of Calculus”. For the rest of Leibniz life, he would fight to prove that he invented calculus first and independently of Newton. Only on more recent years can we give the credits he deserved.

Now, we may all love a good fight such as this one but, we’re forgetting the most important thing: two persons independently came to calculus! What other proof do you need to believe math is the language of the universe?

Now, back to Newton.

Newton on Gravity

As already wrote in the last article (), Newton was talking to Edmund Halley when asked “Why do planets move in ellipsis?”. Newton thought for a second and said “Hold my bear please” and 18 months later came back with the answer: Universal Theory of Gravity.

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When an apple fell on Newton’s head

In his work Newton stated his three laws of motion, laying down the foundation for classical mechanics. He also came to the conclusion of some really important stuff. He would provide another proof for heliocentrism, showing that according to his theory, the sun must be the center of the Solar System. However, Newton would also realize the Sun cannot be center of the Solar System. What I mean by this is that Newton believed no body could be at rest, and so a “center” of anything. Newton rather thought it as “the common center of gravity of the Earth, the Sun and all the planets is to be the esteemed the center of the World” (which is very close to the Sun).

Now finally, let’s get technical!

Newton’s first Law of Motion – Inertia

In states that “an object in motion will remain in motion, and an object at rest will remain at rest, unless acted upon by a force“. This basically means that you need a force to take an object out of its initial state (at rest for example). How hard it is to move the object depends on the object’s inertia. You can measure inertia via the objects mass. The more mass an object has, the harder it is to move!

This is better explained in the second law of motion.

Newton’s second Law of Motion

It states that “net force is equal to mass time acceleration” or as an equation:


Where F is the net force appliedm is the mass of the body, and a is the body’s acceleration. Thus, a net force applied to a body produces acceleration. In the same way, when a object is accelerating it means a force is being applied to it.

Probably the most common and intuitive case of a net force producing acceleration is the gravitational force. Imagine you through a 2 kilogram coconut (because, who doesn’t like coconuts?) straight up in the air. After a second or two, the coconut will start falling due to the gravitational force with an acceleration of about 9.81 m/s^2 (if there is no wind and of course we neglect air resistance).

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Just if you need help imagining a coconut

So, if gravity is the only force acting on the coconut, we can calculate the force of gravity by using F=ma. So the formula will became


Where Fg is now the gravitational force and g the rate of acceleration, 9.81 m/s^2. Now we can calculate the force of gravity:

Fg=mg = 2kg (9.81 m/s^2) = 19.62 kg(m)/s^2 = 19.62 N

And this is how you determine the force of gravity, or the weight of something. Now, those units are a bit too much, so we just call it Newtons (N, as you saw above) in honor of Sir Isaac Newton.

Now, usually gravity isn’t the only force on action, so we must take into account other forces. This’s where we get to a force that tends to show up a lot, which is explained by Newton’s third Law.

Newton’s third Law of Motion

For every action, there is an equal but opposite reaction“. You should know this one from about ten thousand memes right? But there is more to this law than just that.

We call this reaction force the normal force (N), because it’s perpendicular to whatever surface your object is resting on.

This reaction force is different from other forces (like gravity) however. It’s kind of special. The thing is, the magnitude of the reaction force changes.

Imagine a box on the ground. The box has a weight of 10 N, so it pushes on the ground with a force of 10 N. Now, why doesn’t the box fall through the ground? Because of the reaction force, which pushes back on the box with a equal force (10 N).

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where N is the nomal force and W is the weight of the box. Both forces are equal and opposite

If the weight of this box was 20 N, the ground would push back with the same magnitude. This will happen on and on, until the ground can’t counteract anymore and it breaks.

I hope you have liked this article. If you did (or if you didn’t) please comment on your thoughts about it!

Baltas Cruz

Baltas Cruz

He is a 15-year-old Portuguese with pretensions to becoming a theoretical physicist. He is also a chess player with some prizes in local competitions as well as a runner in a local team. Basically, a young man that loves life and lots of interesting stuff like PHYSICS.

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