Newton's Second Law of Motion

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This is a basic physics tutorial that is targeted at GCSE (grade 9 and grade 10) standard, covering the basics of Newton's Second Law of Motion. The associated video tutorial is on its way.

What is Newton's Second Law of Motion?

We've learned that until a force is applied to an object, it will continue to do what it is already doing - either stay at rest, or move at a constant velocity. When a force is applied to it, there is a change in that velocity. Any change in velocity is a form of acceleration.

Newton's Second Law of Motion tells us that there is a relationship between an object's mass, the magnitude of the force that's applied to it, and the resultant acceleration. It states that:

The relationship between an object's mass m, its acceleration a,
and the applied force F is F = ma.

What does F = ma tell us?

It tells us that any change in the magnitude of the force that's applied to an object will result in a proportional change in the resultant acceleration.

Take an object with a mass of 2 kg. If you were to apply a force of 10 N to the right to it, what would the resultant acceleration be?

You need to do some simple rearrangement of the formula f = ma to get your answer; mouse over the image below to see the steps outlined in more detail.

What happens if you change the force?

The formula f = ma tells us that if you tripled the force (to 30 N to the right), the resultant acceleration would also triple (to 15 m/s2 to the right).

This means that the change in acceleration is directly proportional to the change in force.

What happens if you change the mass?

If you changed the mass of the object, but kept the force constant, the change in acceleration would be inversely proportional to the change in mass. Take this object for example with a mass of 1 kg. If you applied the same force of 30 N to the right to it, it would result in an acceleration of 30 m/s2 to the right.

Notice how the mass of this object is half that of the one in the example above, but the resultant acceleration from a force of 30 N is double? This confirms that the variables of mass and acceleration are inversely proportional to one another.

How will I remember this?

When you first start to learn about all of this, it can seem a little confusing. Don't worry, we've all been there - and some of us still are! Just know that all you need to remember is the formula f = ma. You can use simple algebra to manipulate this equation to work out what would happen to a system if you change any of the variables.

To get you feeling comfortable with this formula, why not get practising with the exercise worksheet below? Once you're feeling confident, you can move on to learn about Newton's Third Law of Motion.

Exercise Worksheet

This worksheet has 9 exercises that you can work through in your own time, with answers worked out for you to compare your own answers (and working out) against. To download the document visit Slideshare here: