Newton's Laws of Motion

Newton's first law of motion roughly states that:

A body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force.

So, what does this mean? Well, let's take a weird hypothetical scenario and imagine we have a basketball in a gigantic frozen lake. If we carefully place the basketball on the frozen lake, nothing happens as it stays at rest. However, let's say we roll the ball across the lake. The ball will slide with the same speed across the lake until it reaches the end of the lake because no external force acts on it to change its velocity. Friction usually stops objects like basketballs from rolling indefinitely but the frozen lake is assumed to be frictionless, meaning the ball will continuously roll forever until it eventually reaches one of the lake's ends. This is Newton's first law of motion in practice.

Note that being at a constant velocity also means that the object won't change direction or speed. Also note that the law mentions "external net force", not just force. This means that you can apply force on an object and still keep it in constant velocity or at rest. However, you have to apply multiple forces such that they cancel out.

All of Newton's laws are experimentally proven thoroughly to be universal, dictating the way planets and moons move along with ordinary Earth-based objects.

This law is often known as the law of inertia because it has to do with a property of objects known as inertia. Inertia is the given tendency of an object to remain at rest or stay at constant velocity if no net force acts on it. The way to measure inertia is through the mass of an object. Of course, in the traditional sense, mass is defined as the measure of matter in an object but it can also measure how resistant an object is to acceleration(change in velocity). Inertia is why it's much harder to move a truck than a tennis ball, for example.

Newton's Second Law of Motion is similar to Newton's First Law, but is more quantitative. However, interestingly enough, the 2nd law indirectly proves the 1st law.

Newton's Law states that the net force applied on an object is equal to the rate of change(derivative) of the momentum of the object with respect to time. This also means the rate of change of momentum with respect to time is in the same direction as the applied net force.

Newton's Law can be applied to changes in momentum in any dimension(x,y,z).

Using this same definition, we can derive a more easy-to-use definition of net force. Note that change in momentum is the product of an object's mass and change in velocity. Since mass can be taken as constant, the change in mass of an object is 0. The change in velocity over change in time is just acceleration. Thus, the derived form of net force can just be:

If you've ever gone swimming and were up against the wall, you may have pushed your feet against it to propel yourself forward. This is a prime example of Newton's Third Law, which popularly states that every reaction has an equal and opposite reaction. This means that if Object 1 exerts a force on Object 2, Object 2 exerts a force equal in magnitude but opposite in direction back on Object 1. Note that the reaction force is also of the same type as the action force.

For example, the gravity of the Earth pulling on you is equal to the gravitational force you exert on the Earth. However, from Newton's 2nd law, since the Earth's mass is so high, its acceleration due to the force you exert on it is negligible.

Now, using the example above, the force you exert on the wall when swimming is equal in magnitude to the force that the wall exerts on you. However, the wall exerts a force in the opposite direction so you push forward.

A common misnomer with Newton's Third Law is that the action and reaction force should cancel out. However, this is why systems are important In the example with the swimmer, you exert a force on the wall, so the wall and the wall ONLY will feel the force. Similarly, when the wall exerts a force on you, you and you ONLY will feel that force.