Before going any further, here's a warning about Newton's laws and frames of reference.

On the ground, I drop a ball and it falls down.

I throw a ball and it behaves like a projectile, it travels in a vertical plane.

But if I were on a merry-go-round, I'd see the ball curve to the side.

There's no horizontal force acting, yet from my point of view,

it is accelerating sideways.

Newton's laws don't work in that frame of reference.

It's called a non-inertial frame.

A frame of reference in which Newton's laws do work, is called an inertial frame.

Wherever you are, you can always find an inertial frame of reference.

Here's a tip.

Looking up from the merry-go-round, we'd see that the stars seem to be moving in circles,

i.e. they're accelerating.

For an observer in an inertial frame, the distant stars are not accelerating.

To say more than that takes us into a subject called relativity,

which is not in our syllabus.

However, we do have multimedia resources about relativity for you.

Newton's second law is often written as an equation.

For a body of mass, "m", accelerating at "a", the total force, "F-total," is "ma."

Acceleration, we've already met.

It's a vector.

The total force is a vector, and it's parallel to the acceleration, "a".

On the other hand, the mass is a scalar.

Here's something very important.

Mass is not the same thing as weight.

My mass is 72 kilograms, and it depends on how many and what sort of atoms I'm made from.

Weight is a force, it's a vector.

On earth, my weight is 700 newtons,

and its direction is in the direction of the earth's gravitational field.

We call that direction down.

On the moon, where the gravitational field is about six times smaller,

my mass would still be 72 kilograms, but I'd weigh 120 newtons.

Weight depends on the strength and direction of the local gravitational field,

as well as on the mass.

A liter of water has a mass of one kilogram.

So does this block of iron.

They both weigh 9.8 newtons.

Mass is a scalar, weight is a vector, and its direction is down.

More on that later.

By the way, Americans use pounds for force and slugs for mass.

We explain the conversions on our resource pages.

In physics, we all use newtons and kilograms.

The equation, "F-total equals ma", tells us three things.

The greater the total force you apply for an object, the faster it accelerates.

But the greater the mass of an object,

the smaller the acceleration given to a total force.

Finally because it's a vector equation,

the acceleration is parallel to the total force applied.

The standard unit of force is the newton, named to honor Isaac.

One newton accelerates one kilogram at one meter per second per second.

Humans can comfortably exert forces as large as a few kilonewtons,

and we can feel forces less than a millinewton.

But we can be more quantitative.

We've shown that, in freefall, objects accelerate downwards at "g",

or 9.8 meters per second per second.

Applying Newton's second law gives us the force acting in free fall.

That force is called an object's weight.

So the weight is in mg, and its direction, by definition, is downwards.

How big are the units of force?

The weight of a nectarine is about one newton.

The weight of an adult is usually between half and one kilonewton.

The weight of this piece of paper is about one millinewton.

This one, about one micronewton.

Why not get some scissors and paper and see whether you can feel the micronewton?

Look at the equation we're using for Newton's second law.

If we set "F-total equals zero," then "a equals zero."

So this one equation states both the first and the second law.

First law, second law.

Well, you can guess what's coming next.

But first, as usual, there's a quiz, and before that, a serious puzzle for you.

Here's something that worried me when I first met Newton's laws.

The second law is subtle.

"F-total equals ma" is our definition of mass.

Mass is the ratio of the total force on an object to the acceleration it produces.

But it's also our definition of force: F-total equals ma.

Superficially, doesn't that make it look as though the law is true by definition?

Yet we call it a scientific law, which means that it has to be, in principle, falsifiable.

Can you see how that's possible?

Try to answer this yourself before you go to our explanation.

Try hard.

I want it to puzzle you as much as it puzzled me when I first thought of it.