What are Newton's laws of motion? Three rules, explained

Newton's laws of motion are three rules that describe how objects move when forces act on them. First, an object keeps doing what it is doing, resting or moving in a straight line, unless a force changes that. Second, force equals mass times acceleration. Third, every force comes with an equal and opposite force. Isaac Newton published them in 1687, and they still put satellites in orbit.

In short

• A force doesn't keep things moving; it changes how they move. With no force, motion carries on unchanged.
• The same push speeds up a light object more than a heavy one, in exact proportion: F = ma.
• Forces always come in pairs acting on two different objects, which is how a rocket pushes itself forward.

Where do the three laws come from?

Newton set out the laws at the start of the Philosophiæ Naturalis Principia Mathematica, usually called the Principia, first published in 1687 and revised in 1713 and 1726. As the Stanford Encyclopedia of Philosophy notes, his first law reads "Every body perseveres in its state of being at rest or of moving uniformly straight forward" unless forces compel it to change. The tidy equation F = ma appears in no edition; it is the modern way of writing his second law.

Newton built on others. Galileo had already argued that a ball rolling on a smooth level surface would roll on forever if nothing slowed it, which overturned the ancient idea, going back to Aristotle, that motion needs a constant push. What Newton added was a single system: three laws plus a law of gravity that explained falling apples, the tides and the paths of the planets with the same mathematics. That is the kind of testable, general explanation science looks for.

What does the first law say?

The first law is the law of inertia: an object at rest stays at rest, and an object in motion keeps moving at the same speed in a straight line, unless a net force acts on it. Inertia is the tendency to resist changes in motion, and the more mass something has, the more inertia it has.

Everyday life hides this law, because friction and air resistance are always slowing things down. A hockey puck on ice glides a long way because ice gives little friction. In space, where there is almost nothing to slow it, a probe coasts for decades: once its engines stop, it keeps going with no fuel spent.

A seatbelt is the first law made practical. When a car stops suddenly, your body keeps moving forward at the car's old speed. The brakes act on the car, not on you; only a force applied to you, by a belt, an airbag or the dashboard, can stop you.

What does the second law, F = ma, mean?

The second law says how much a force changes an object's motion. The acceleration of an object equals the net force on it divided by its mass: a = F/m, more often written F = ma. Force is measured in newtons: one newton is the force that speeds up a 1 kg mass by 1 meter per second, every second.

Push an empty shopping cart of 10 kg with a force of 20 newtons and it accelerates at 2 m/s². Fill it to 40 kg and the same push gives only 0.5 m/s². Four times the mass, one quarter of the acceleration. That is why a loaded truck needs far more braking force than a bicycle to stop in the same distance.

A worked example: why seatbelts save lives

Take a 70 kg passenger in a car going 50 km/h, which is about 13.9 m/s, that hits a wall. With a seatbelt, the passenger stops along with the car's crumple zone and the belt's stretch, over roughly 0.5 m. The deceleration is speed squared divided by twice the distance: 13.9² ÷ (2 × 0.5) ≈ 193 m/s², about 20 times the pull of gravity. By F = ma, the belt pushes on the passenger with about 70 × 193 ≈ 13,500 newtons, spread across the chest and hips.

Without a belt, the passenger flies on until the steering wheel or windshield stops them, over perhaps 5 cm. The same arithmetic gives about 1,930 m/s² and a force of about 135,000 newtons, ten times larger and concentrated on a small area. Stopping over a longer distance means a smaller force. Seatbelts, airbags and crumple zones are all designed around that one line of the second law. (The figures are rounded for illustration; real crashes vary.)

What does the third law say?

The third law says that when one object pushes on another, the second pushes back on the first with a force of the same size in the opposite direction. The two forces act on different objects, which is why they don't cancel out.

A rocket works this way. Its engines push hot gas out of the nozzle at high speed, and the gas pushes the rocket the other way. It needs no air to push against, which is why rockets work in space. The same pair of forces lets you walk: your foot pushes the ground backward, and the ground pushes you forward.

Do heavier objects fall faster?

No, and this is the most common misunderstanding of Newton's physics. A heavier object is pulled by gravity with more force, but it also has more mass to accelerate, and by the second law the two cancel exactly. With no air resistance, every object falls with the same acceleration, about 9.8 m/s² near Earth's surface.

On Earth a feather falls slowly because air pushes back on its large surface. On the Moon there is no air, and in 1971, on the Apollo 15 mission, astronaut David Scott dropped a 1.32 kg hammer and a feather together in front of a television camera. NASA's record of the drop describes the result: they accelerated the same way and hit the ground at the same moment.

How do Newton's laws explain orbits?

An orbit is falling forever while moving sideways fast enough to keep missing the ground. Newton pictured a cannon on a tall mountain. Fire a ball slowly and it lands nearby. Fire it faster and it lands farther away. Fire it fast enough and the ground curves away beneath it as quickly as it falls, so it never lands.

The first law says the ball would fly off in a straight line; gravity, a force, keeps bending its path toward Earth; the second law says by how much. The International Space Station does exactly this, moving at about 8 km (5 miles) every second and, as NASA puts it, circling Earth about every 90 minutes. Astronauts on board float not because gravity is absent, which at that height is still about 90% as strong as on the ground, but because they and the station are falling together.

Where do Newton's laws stop working?

Newton's laws are extremely accurate for everyday speeds and sizes, and engineers still design bridges, cars and spacecraft with them. They break down in three places.

Near the speed of light, time and length change in ways Newton's laws don't allow, and Einstein's special relativity takes over. In strong gravity, Newton's picture of gravity as a pull between masses gives way to general relativity's curved spacetime: Mercury's orbit swings around the Sun by about 43 arcseconds per century more than Newton's laws predict, a gap that Albert Einstein explained in 1915. And at the scale of atoms, quantum mechanics replaces exact paths with probabilities.

Each newer theory reduces to Newton's laws at ordinary speeds, distances and sizes. That's why they are still taught first: they are not wrong, they are a limit of something more complete. They also leave out what happens to energy as heat and friction wear motion down, a question for entropy.

Check yourself

• Without looking back: why does a passenger without a seatbelt keep moving when the car stops?
• If the third law gives equal and opposite forces, why don't they cancel out?
• Explain to a friend why a hammer and a feather hit the Moon's surface at the same moment.

Sources

• Newton's Laws of Motion — NASA Glenn Research Center
• Newton's Philosophiae Naturalis Principia Mathematica — George Smith, Stanford Encyclopedia of Philosophy, 2007
• The Apollo 15 Hammer-Feather Drop — NASA Space Science Data Coordinated Archive
• Space Station Facts and Figures — NASA
• Newton's laws of motion — Wikipedia