# Newtons Laws of Motion

Not only the greatest mathematician of the late 17th early 18th century, but arguably one of the greatest mathematicians of all time. With extensive work on the foundations of calculus, the discovery and application of universal gravitation and what i shall now discuss with you here: Newton’s Laws of Motion. His 1687 publication, Philosophiæ Naturalis Principia Mathematica, detailed (amongst many other things) these three laws which form the basis for classical mechanics and were not to be improved upon for over 200 years, quite a remarkable feat for a 17th century mathematician and physicist.

Philosophiæ Naturalis Principia Mathematica not only stated and explained the laws of motion, it also showed how, when combined with Newton’s law of universal gravitation, they were able to explain Kepler’s laws of planetary motion. So what are Newton’s three laws? Well read on and all shall become clear.

Newton’s First Law: Law of Inertia

“A body will remain at constant uniform velocity (or at rest) until it is acted upon by a net external force”

But what does this actually mean? Well, to put it very simply, it means that unless you apply a force to make something move faster or slower (and remember, friction is a force that acts on everything to slow it down) then you will stay at rest or move at a constant speed in a straight line.

Newton’s Second Law:

“The magnitude of the Force applied to a body is equal to the rate of change of momentum” (Momentum is simply the mass of an object multiplied by its velocity)

This was a break through in physics, as it was previously thought that force was needed to maintain motion, but Newton claimed (and rightly so) that Force was only needed to change an objects motion. Now with a bit of maths involving basic first order differential equations, you can deduce (as Newton did) that the force is equal to the mass of the object multiplied by the acceleration it experiences due to the force. So the more force you apply to an object, the more quickly the object accelerates.

Think of a car. The more you put your foot down on the accelerator, the more force you are applying to the car and the faster you accelerate. This is of course, all dependent on how heavy your car is, i.e. how much mass it has. Simple.

Newton’s Third Law:

“Every action has an equal and opposite reaction”

The one we all love to quote. Meaning? Well, exactly what it says on the tin. Basically, if you are sitting on a chair reading this article, you are applying a force on the chair (your weight) and the chair is applying a force which is the same magnitude (strength) but in the opposite direction to keep you sitting on the chair.

The classic example is the recoil of a firearm. Here, the force that sends the bullet forward is applied back on the gun in the opposite direction (and is therefore felt by the person firing the gun) Now because the bullet and the gun have different masses, according to Newton’s second law, they have different accelerations (as the force is the equal and opposite)  and therefore the lighter bullet accelerates very quickly away from the gun, and the gun itself, being heavier, recoils and is felt by the shooter.

Newton’s laws are all universal, which means that they apply everywhere in the universe and are not affected by where you are in the world or what time of day you test them. His laws do however, only apply to bodies that can be considered as ‘ideal’ or as ‘particles.’ Basically, such that the object in question is small in relation to the distance it is moving through, and this is why things such as the motion of planets in orbit around the sun can be described using Newton’s Laws.

Where Newton’s Laws fail:

I mentioned earlier that these laws have held for over 200 years, this was until Einstein, in his work on the Special Theory of Relativity, considered Newton’s Laws of Motion at speeds approaching the speed of light. But for speeds that are ‘non-relativistic’ (i.e. not near the speed of light) Newton’s Laws remain to this day, an excellent approximation to the motion of all objects.