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## Newton’s 2nd law of motion, force and acceleration

Last week, I blogged about Newton’s 1st law of motion, and the concept of inertia. At the end I said that this week I would discuss what happens to an object if a force is applied. Or, to put it more correctly, an “external resultant force” is applied. This is what Newton’s 2nd law of motion is all about – the effect on a body of an applied force.

Newton’s three laws of motion appear in his masterpiece, The Principia, which was published in 1687.

If we apply a force to an object it will change its velocity, which means it will accelerate. As I have mentioned before, in physics acceleration has a more precise meaning than it does in everyday life. It doesn’t just mean an object is changing its speed, it can also be keeping a constant speed but changing its direction, such as an object moving at a constant speed in a circle. But, whether an object is changing its speed or changing its direction, it has to accelerate to do this, and so a force needs to be applied.

## The most important equation in physics

The relationship between force and acceleration is given by Newton’s 2nd law of motion, which states that

$\boxed{ F = m a }$

where $F$ is the force, $a$ is the acceleration, and $m$ is the mass of the body. From this equation, along with Newton’s 3rd law (which I will discuss next week), nearly all of mechanics can be derived. For example, this equation tells us that for the Moon to orbit the Earth, it must have a force acting upon it. That force is gravity, and Newton was also the first person to produce an equation to describe gravity. For example, in this blog I showed how we can derive the acceleration felt by a body travelling in a circle, which we call the centripetal acceleration.

Using calculus, this equation also allows us to derive the three equations of motion, equations like $v = u + at$ and $s=ut + \frac{1}{2}at^{2}$, as I did in this blog. It tells us that it is more difficult to accelerate a more massive object than it is a less massive one, which is why you need a more powerful engine in a large truck than you do in e.g. a small car. Along with Newton’s 3rd law, it explains why a bullet comes out at such a high speed from the nozzle of a rifle, but why the recoil of the gun moves much more slowly. As I said, the most important equation in physics.

Next week I will discuss the last of Newton’s laws of motion, his 3rd law.