What are Newton's laws of motion?

In 1687 Isaac Newton wrote down three rules that describe how everything moves, from a cricket ball to the Moon.

1. The law of inertia. Something that is still stays still, and something that is moving keeps moving in a straight line at the same speed, unless a force acts on it. A puck on ice slows down only because friction pushes back on it. Take the friction away and it would glide for ever. This laziness of matter is called inertia.

2. F = m × a. A force makes things accelerate, which means change their speed or direction. Twice the force, twice the acceleration. Twice the mass, half the acceleration. Force is measured in newtons (N): one newton gives 1 kg an extra 1 m/s of speed every second. A newton is about the weight of a small apple.

3. Action and reaction. Forces come in pairs. When you push on something, it pushes back on you just as hard, the other way. Two skaters who push apart both move, and the lighter one moves faster.

A useful quantity ties them together: momentum, p = m × v. A force changes momentum, and in a push between two things, what one gains the other loses.

When a car stops suddenly, you don't. Nothing has pushed on you yet, so by Newton's first law you carry on at the car's old speed. That's why passengers lurch forward when a bus brakes hard. See CarClear.

In a crash at 50 km/h the car's front crumples by about 60 cm, so the cabin stops in under a tenth of a second. A seat belt catches you early and stretches a little, so you stop over about 90 cm, together with the car.

Without a belt you keep going at almost the full crash speed until you hit the steering wheel or windscreen, which stops you in a few centimetres. The same change of momentum squeezed into a much shorter time means a much bigger force: F = Δp ÷ Δt. Stopping in 5 cm instead of 90 cm takes more than ten times the force.

A piano hammer uses inertia on purpose. The key's jack throws the hammer and then lets go about 2 mm before the string, so the hammer flies the last bit on its own and can bounce straight off. It touches the string for only a thousandth of a second or so, and the string pushes it back just as hard as it hits. See PianoClear.

Newton's second law tells you how fast anything can speed up: a = F ÷ m. The tyres push backwards on the road, and by the third law the road pushes the vehicle forwards. What's left after air drag and rolling resistance is the force that accelerates it.

At the start, a family car's tyres can push about 6,900 N on its 1,300 kg, and a 150 cc motorcycle about 1,100 N on its 215 kg with rider. That's roughly the same acceleration, about 5 m/s². But once they are moving, force is limited by power: F = P ÷ v. The car has about 85 watts per kilogram, the motorcycle about 48, so the car pulls away. See CarClear and MotorcycleClear.

Turning is accelerating too, because the direction of your velocity changes. To go round a circle of radius r at speed v you need a push towards the middle of F = m × v² ÷ r. On a road that push comes from the tyres' grip. A motorcycle or bicycle leans so that gravity and the road's push line up: tan θ = v² ÷ (g × r). See MotorcycleClear and CycleClear.

Newton's third law says forces come in pairs. If A pushes B, then B pushes A just as hard, in the opposite direction. The two forces act on different things, so they don't cancel out.

A dishwasher's spray arms have no motor. The little holes are drilled at a slant, so each jet shoots out backwards and a little sideways. The arm pushes the water back; the water pushes the arm forward. Ten tiny pushes add up to enough twist to spin the arm. See DishwasherClear.

A fan works the same way with air. Its blades throw air forward, and the air shoves the fan backwards. Stand a desk fan on a skateboard and it rolls away from its own breeze. A ceiling fan pushes air down, so the air pushes it up: a big one hangs about 1.3 kg lighter when running. See FanClear.

A rocket is the purest example. It throws hot gas out of the back at thousands of metres per second, and the gas throws the rocket forward. It needs no air to push against, which is why rockets work in space.

Even walking is the third law. Your foot pushes the ground backwards, and friction from the ground pushes you forwards. On slippery ice there is little friction to push you, so you can't get going.

Newton's laws have sent people to the Moon, but they are not the last word.

Very fast. In 1905 Albert Einstein showed that momentum is really p = γmv, where γ = 1 ÷ √(1 − v²/c²) and c is the speed of light. At everyday speeds γ is 1 to many decimal places, so Newton is perfect. At 10% of light speed γ is 1.005, at half light speed 1.155, and at 90% it is 2.29. Push harder and harder and you add momentum, but the speed only creeps closer to c, never past it. Protons in the Large Hadron Collider have γ of about 7,000.

Very small. Inside atoms, electrons don't follow neat paths at all. They are described by quantum mechanics (1925 onwards), which gives chances rather than certainties. Newton's laws come back once you average over huge numbers of atoms.

Spinning rooms. Newton's laws hold for someone who isn't accelerating. Inside a spinning washing machine drum, water seems to be flung outwards by a "centrifugal force". Watched from outside, nothing pushes it out: the drum stops pushing it round, and it simply carries straight on through the holes. That's the first law again. See WasherClear.

Myth-buster: “Heavy things fall faster.” Aristotle thought so, and it feels right. But a heavier object has more weight and more inertia, and the two cancel: a = F ÷ m = mg ÷ m = g. Only air resistance slows a feather. On 2 August 1971, astronaut David Scott dropped a hammer and a falcon feather on the Moon, and they hit the ground together.