Newton's second law

Force changes motion in a simple world

When the motion changes, that's when we need to provide an explanation.

Natural motion – occurring in a stripped-down environment – is simple: there is no acceleration. And physics seeks to understand the simple first, by refining the model or description of the world, then – and only then – adding complexity to the model to predict how the object will behave in a less simple environment. We'll return to this extreme simplicity in a while, but for now we suggest you consider the next simplest environment for the object: one where there is a single force acting on the object. (You'll recall that we isolated objects from their environments in the SPT: Forces topic, and re-described the interactions with the environment as a single force exerted by the environment on the object.)

This – perhaps the simplest interesting environment – leads to a very deep truth about the world: force, mass and acceleration are linked.

Resultant force sets acceleration: determining the change in motion. The greater the mass of the object, the more this acceleration is impeded. That's how the object's internal property and it's environment jointly determine the change in motion.

There is only one internal property that turns out to be important, and all the environmental factors can be reduced to the resultant force.

Here is how we suggest you express this great empirical discovery:

acceleration = forcemass

The change in motion is the result of two factors, and two factors only:

• The mass of the object – an intrinsic property of the object.
• The force acting on the object – a single quantity that represents the interaction of the environment with the object.

Acceleration really is the kingpin: it links all the work on forces with possible motions – being able to calculate acceleration is an end point for all that work on forces.

Acceleration, force and mass

This is a fantastic intellectual achievement: it's a great empirical discovery.

It's best written like this:

acceleration = forcemass

By choosing to write it in this way you emphasise that the dependent variable, the acceleration, is the result of other choices that you make. We like using mathematics to emphasise the physics.

However, the relationship presupposes that you understand the world to which it applies: that is, the Newtonian world. It happens that this world mimics the lived-in world particularly well, so long as you fully understand how to describe things in the lived-in world in terms that are Newtonian. You have to get good at translating between the two languages, or seeing the world in a different way. The SPT: Forces topic and the SPT: Motion topic were preparations for that. Here we're suggesting that you think a little more about exactly what's being done so that students can see that it's useful but not obvious or necessary.

Being able to predict how the motion of objects changes (that is, calculating the accelerations of the objects) is very useful.