Newton's first law of motion and inertia

A question about the bus

You stand in a moving bus and the driver brakes hard. You lurch forward. Nobody pushed you. Why did you move?

Newton's first law

An object stays at rest, or keeps moving in a straight line at a steady speed, unless an unbalanced force acts on it.

1. At rest, it stays at rest. A book on a table does not start moving by itself.
2. Moving, it keeps moving at the same speed in the same direction.

In the bus, the floor stops your feet, but nothing stops the top of your body, so it carries on forward.

"But things always stop!"

A rolling ball stops because friction and air act on it: an unbalanced force. Make the floor smoother and it rolls further. With no friction at all, it would never stop.

You should find that halving the slowing doubles the distance. As the slowing gets close to zero, the distance grows without limit: that is the first law.

Inertia

Inertia is the way an object keeps doing what it is doing. The more mass it has, the more inertia: a loaded truck is much harder to start or stop than a bicycle.

Watch out. The first law is not about what 'normally' happens. It describes what would happen with no unbalanced force, and friction is a force.

A worked example

A puck slides off at $6\ \text{m/s}$ on four floors that slow it by $3\ \text{m/s}^2$, $1\ \text{m/s}^2$, $0.2\ \text{m/s}^2$ and $0.02\ \text{m/s}^2$. How far does it go on each?

1. Carpet. $\dfrac{(6\ \text{m/s})^2}{2 \times 3\ \text{m/s}^2} = 6\ \text{m}$. Wood. $\dfrac{(6\ \text{m/s})^2}{2 \times 1\ \text{m/s}^2} = 18\ \text{m}$.
2. Ice. $\dfrac{(6\ \text{m/s})^2}{2 \times 0.2\ \text{m/s}^2} = 90\ \text{m}$. Air track. $\dfrac{(6\ \text{m/s})^2}{2 \times 0.02\ \text{m/s}^2} = 900\ \text{m}$.
3. So the smaller the friction, the further it goes: with none, it would go on for ever.

Practise with new numbers

Try it in Python

The program works out the four floors.

Remember these

• First law: no unbalanced force, no change in motion.
• Things stop because of friction, which is a force.
• Inertia is the tendency to keep the same motion; more mass, more inertia.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A card is flicked from under a coin on a glass. Why does the coin fall into the glass?

2. Why do you lean to one side when a bus turns a corner sharply?

3. Which has more inertia, a football or a cricket ball of the same size? Why?

4. A spacecraft far from any star switches off its engines. What happens to its motion?