**Introduction**

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.

This is the **eleventh article** in the** Beginning of Physics serie**s. 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**!

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.

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**.

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 tha**t 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:

**F**=*m***a**

Where **F** is the **net force applied**, *m* 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).

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

**F**g=*m***g**

Where **F**g 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**).

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!