Newton's second law

This short post is a little break in my current series on light. It came about because I got to thinking about Newton's law of gravity, which got me thinking of Newton's laws of motion. Which got me thinking about Newton's second law of motion.

Newton's second law of motion results in one of my favourite equations of all time. It is fabulously simply and yet gives one of the most profound insights into the nature of the universe.

You may be thinking at this point that I am getting a little carried away, but I don't think I am and here is why.

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


This was how Newton first stated his second law. According to a Wiki entry the modern equivalent of this is

The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.

This just doesn't do it justice though. Now, if you have read any of my other posts you may have noticed that I sometimes have a bit of a moan about mathematics and its place in science, but on this occasion I freely admit that only mathematics allows us to do write this law in a manner that portrays its true wonder. Here it is (see the image above if you haven't already guessed) ...

F = m a

F - force applied
m - mass of the object
a - acceleration.

That is it. That is all there is to it. A single line with only 3 terms.

It tells is that the resulting acceleration is directly proportional to the applier force.

This means that if we push an object it will accelerate away from us. If we push it twice as hard it will accelerate at twice the rate. Push it 10 times harder and it will accelerate 10 times faster.

It also tell us that if the object as twice the mass then we need to apply twice the force to get the same acceleration.

Let's just have a think about that for one minute. We live in a universe where if we push something it will start to accelerate, once we stop pushing it will immediately stop accelerating, although it will continue moving at the same velocity, unless acted upon by another force, friction for example.

This is how the universe works!

What is odd for me is that these days we have something called the conservation of momentum and we can derive Newton's second law from this, so it sort of makes Newton's second law redundant. It is no longer "required" in fundamental theories within physics.

Personally I think this is a mistake. See what we appear to be saying is that Newton was undoubtedly brilliant for point out his second law. But it is not really necessary after all.

It is true that we can derive the above result from conservation of momentum, but I think this actually robs us of something because we are not seeing force any longer.

We are seeing momentum and energy and this does give us some greater insight.

In a way though I think that while we are able to see the trees in far greater detail, we are maybe losing site of the knowledge that it is a forest and what this can tell us about the over all system.

F = m a

how utterly simple, how amazingly brilliant.