Newton's Laws

There has not been a more complete contribution to the field of mechanics since Sir Isaac Newton defined the basic laws of motion. The real beauty of these laws which now bear his name is that they can explain how an apple falls off a tree to the group as simply as they can describe how the moon moves around the earth. In fact, it was that very juxtaposition that got him thinking about it in the first place.

Before him, no one could understand what kept planets and moons in their orbits. They weren't connected to anything, so explaining why they didn't fly away was a difficult proposition. But watching the apple fall led him to understand the fundamental principles of forces. I'll define the laws and then use them to explain this phenomenon.

The First Law

Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

The first law can be described in several different ways. We can say, as is often said, that objects at rest will stay at rest and objects in motion will stay in motion until acted upon by an outside force. Another way to say this is to say that something changes velocity only when another object is applying a force. Most simply, this law describes a characteristic of mass known as inertia (which is its propensity to stay in motion unless acted upon).

This law explains that the natural motion of an object with velocity is a straight line, which is not as obvious as one might think. Before forces were well understood (i.e. before Newton), it was easy to think that forces tended to travel in curves (just throw a ball in the air) and that straight line motion was anomalous. Thus, by logic we can assume that anything moving in anything other than a straight line has a force acting on it.

The Second Law

Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

The second law describes the effect of forces on masses. Specifically, the amount force on an object can be quantified by multiplying its mass by its acceleration. Succinctly, we say that F = ma. Here we learn an important characteristic of mass: it resists change. The larger the mass, the larger the force required to cause it to accelerate as quickly as a smaller mass.

The first law is just a special case of the second law. That is, the first law is simply a description of what happens when F = 0. By the second law we know that ma = 0, and since we know the object has a non-zero mass (it being an object), we must conclude that there is no acceleration. In other words, something with no forces acting on it cannot change velocity (whether moving or not).

The Third Law

Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi.

You know this one, too. In fact, I've never met a person to whom I could say the first half without having the second half repeated to me. For every action (applied force) there is an equal force applied in the opposite direction. We sometimes finish that sentence with "...there is an equal an opposite reaction," but I prefer to avoid the term reaction, as it can cause misconceptions.

To clarify the terms of the law, nothing can apply a force on another object without having that object exert an identical force on it. To prove this to yourself, stand facing a wall with your toes against it and push as hard as you can without moving your feet. Of course, you move backwards. Why? Because the wall pushed you with the force that you pushed it.

It's easy to over-think this law. If all forces are paired and equal, then how does anything move at all? Why don't all forces cancel out? The answer is contained in the second law. When you push against a train, the train pushes against you. The train having a huge mass (relatively) has an extremely small acceleration. You, on the other hand, have a very small mass and thus your acceleration is much greater. That is why -- as a general rule -- we try to avoid getting hit by trains.

An Application:

Suddenly, very complex situations are rather easy to describe qualitatively. We can see that the moon is not travelling in a straight line, but that it is travelling in a circular motion. By application of the first and second laws we can say that there is a non-zero force acting on the moon which causes its acceleration. By observing an apple fall (which moves toward the earth without being connected to it), we can assume that the moon is similarly falling toward the earth while moving linearly past it thus keeping it in orbit.

But how can we verify this unseen force? How do we know that it is the earth which exerts a force on the moon and not some other thing that we haven't yet discovered. Newton's third law tells us that if the earth exerts a force on the moon, then the moon must necessarily exert a force on the earth. This force is observed in the tides. The moon's gravitational force on the earth causes the envelope of water around the earth to be distorted, egg-shaped. As the earth rotates, the envelope stays oriented towards the moon and we observe varying depths of the ocean depending on the time of day.

This (long) explanation and application of the most basic laws of physics have set the stage for the explanation of every mechanical (moving) system that we have been able to describe. These laws provide the fundamentals of operations for -- off the top of my head -- space travel, jet engines, dishwashers, fork lifts, building construction, airplanes, cars, and many, many more situations.