Inertia and Newton's first law

What keeps a body moving?

Kick a football on grass and it soon stops. Push a trolley and stop pushing: it stops too. So for two thousand years people believed that a moving body needs a push to keep moving. It sounds right. It is wrong.

Galileo's slopes

Galileo rolled balls down one slope and up another.

The ball climbed almost back to its starting height, whatever the second slope's angle. Make the second slope flatter, and the ball rolls further to reach that height. Make it flat, and the ball should roll forever. What stops real balls is friction, not a lack of push.

Try it with a puck on ice.

You should find that halving the friction doubles the slide. With no friction the line goes on straight: a steady speed, for ever.

Inertia and Newton's first law

Newton's first law. A body stays at rest, or moves in a straight line at a steady speed, unless a net force acts on it.

The tendency of a body to keep its state of motion is called inertia. The more mass a body has, the more inertia: a loaded lorry is much harder to start or stop than a bicycle.

Notice the word net. A car cruising at a steady $60\ \text{km/h}$ has forces on it: the engine's push forward, air and road resistance backward. They balance. Zero net force means no change in velocity, not that no forces act.

Watch out. A force changes motion; it is not needed to keep motion. "The ball moves because the kick is still pushing it" is the oldest mistake in mechanics.

Inertia every day

• A bus brakes, and standing passengers lurch forward: their bodies keep moving.
• A bus starts, and they lurch backward: their bodies stay at rest while their feet are carried forward.
• You shake a wet umbrella: it stops suddenly, the drops do not, and fly off.
• A seat belt is needed because a car can stop in a moment, but your body will not.

Inertial frames

The first law is true in an inertial frame: a frame of reference that is not accelerating. The ground is one, to a good approximation. Inside a car that brakes, a ball on the seat rolls forward with no force pushing it: the car is not an inertial frame while it brakes.

A worked example

A woman pulls a suitcase on wheels along a station platform at a steady $1.2\ \text{m/s}$. The handle pulls with $30\ \text{N}$ at $50^\circ$ above the horizontal. What is the total resistance to the motion?

1. Steady velocity. No acceleration, so the net force is zero.
2. Along the ground. The forward part of the pull is $30\ \text{N}\cos 50^\circ = 19.3\ \text{N}$.
3. So the resistance is $19.3\ \text{N}$, backward.

Think first. Why not $30\ \text{N}$? Part of the pull, $30\sin 50^\circ$, lifts the case a little. Only the part along the ground fights the resistance.

Practise with new numbers

Try it in Python

The program gives a puck the same start on rougher and smoother surfaces, and finds how far it slides.

Remember these

• First law: no net force, no change of velocity.
• Inertia is the tendency to keep the state of motion; mass measures it.
• A force is needed to change motion, not to keep it.
• The law holds in inertial (non-accelerating) frames.

Check yourself

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

1. A lift moves up at a steady speed. Is there a net force on it?

2. Why does a hammer head tighten on its handle when you bang the handle's end on the floor?

3. A spaceship far from any star turns its engines off. What happens to its motion?

4. Which has more inertia: a $2\ \text{kg}$ melon moving slowly or a $0.05\ \text{kg}$ stone moving fast?