Newton's Three Laws of Motion
In 1687, the English scientist Isaac Newton published three rules describing how forces and motion relate. They are now called Newtons three laws of motion, and they remain the foundation of nearly all everyday engineering and physics. Cars, bridges, footballs, planes, rockets and even tiny machines all behave according to Newtons rules. Although Einstein later showed that the laws need adjusting for things travelling near the speed of light or near a black hole, for the world we live in they work essentially perfectly. They are one of the most successful scientific ideas in history.
- First lawInertiaThings stay still or moving unless forced
- Second lawF = m x aForce = mass times acceleration
- Third lawAction-reactionEvery action has an equal opposite reaction
- Published1687In the Principia Mathematica
- AuthorIsaac Newton1642-1727, English scientist
- Used byEvery engineerFor 300+ years
Law 1: Inertia
"An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity in a straight line, unless an unbalanced force acts on it."
The simple version: things keep doing what they are doing unless something forces them to change. A book on a table stays still. A puck sliding on perfect ice would slide forever in a straight line. Things only speed up, slow down or change direction when a force pushes or pulls them.
On Earth, almost everything seems to slow down and stop because forces like friction and air resistance are always acting. Take those away (in space, for example) and motion really does last forever. The Voyager probes are still drifting outwards from the solar system 47 years after launch, with no engine running.
The tendency of objects to keep doing what they are doing is called inertia. Heavier objects have more inertia: they are harder to start moving and harder to stop. That is why a lorry is harder to push than a bike.
Law 2: Force, mass and acceleration
"The acceleration of an object is proportional to the force applied to it, and inversely proportional to its mass."
In symbols: F = m x a. Force equals mass times acceleration. Or, rearranging: acceleration = force divided by mass.
This is one of the most useful equations in physics. It tells you exactly how much an object will accelerate under a given force:
- Push a shopping trolley with the same force twice as hard, and it accelerates twice as fast.
- Double the mass of the trolley (with more shopping) and the same force gives only half the acceleration.
- A 10-newton force on a 1-kg object gives 10 m/s2 acceleration; the same force on a 10-kg object gives only 1 m/s2.
This is why small light cars accelerate quickly and big heavy lorries accelerate slowly with similar engines. It is also why the same dose of medication affects a small child differently from an adult.
Law 3: Action and reaction
"For every action, there is an equal and opposite reaction."
When you push on something, that something pushes back on you with exactly the same strength but in the opposite direction. Forces always come in pairs.
Examples are everywhere:
- Stand on the floor: gravity pulls you down at, say, 700 N. The floor pushes you up at 700 N. The forces cancel and you do not sink in.
- Walking: you push backwards on the ground with your foot; the ground pushes you forwards. That forward push is what moves you.
- Swimming: you push water backwards with your arms; the water pushes you forwards.
- A rocket: hot gases shoot downwards out of the engine; the gases push the rocket upwards.
- A jumping fish: the fish pushes down on the water with its tail; the water pushes the fish up.
- A hammer and a nail: the hammer pushes the nail in; the nail pushes the hammer back (you feel the recoil).
How the laws work together
Real-world motion usually involves all three laws at once. Take the example of a rocket:
- Law 1: the rocket sitting on the launch pad is in equilibrium (gravity down, the pad up).
- Law 3: the engines push hot gases downwards; the gases push the rocket upwards.
- Law 2: the upward force from the engines minus the downward force of gravity equals the net force on the rocket. Divided by the rockets mass, that gives the acceleration.
- The rocket lifts off (slowly at first, faster as it burns fuel and grows lighter).
NASA engineers and SpaceX engineers still calculate rocket flights using exactly Newtons three laws, plus a little maths for changing mass and air resistance.
Where the laws break down
Newtons laws work brilliantly for everyday objects: cars, balls, footballs, planets, planes. But they need adjusting in two extreme cases:
- Very high speeds (close to the speed of light): Einsteins special relativity replaces Newtons rules. Time and mass change with speed.
- Very small scales (atoms and electrons): quantum mechanics replaces Newtons rules. Particles behave like waves with probabilities, not definite positions.
For everything in between, including the entire engineering world, Newtons laws are essentially exact and will probably be used for as long as humans exist.
Deeper dive: Newtons life and apples
The story of Isaac Newton watching an apple fall and suddenly inventing gravity is one of the most famous in science. The truth is a bit more interesting (and slightly less dramatic) than the legend.
Newton was born in 1642 in the small Lincolnshire village of Woolsthorpe. He went to Cambridge University in 1661 to study, but in 1665 the Great Plague forced the university to close. Newton went home to Woolsthorpe for nearly two years and used the time to think about science. He later called this period his annus mirabilis, his "wonderful year".
During this time he made fundamental breakthroughs in three completely different fields:
- Mathematics: he invented calculus (although the German mathematician Leibniz independently invented it a few years later, leading to a bitter priority dispute).
- Optics: he showed that white light is made of all the colours of the rainbow, by passing sunlight through a prism.
- Mechanics and gravity: he began working out the laws that would later become his three laws of motion and the law of universal gravitation.
The apple story comes from Newton himself, who told it in later life to several friends. He said he had watched an apple fall from a tree in his mothers garden at Woolsthorpe and wondered why apples always fall straight down to Earth and never sideways. This thought led him to imagine the same force pulling on the Moon (which falls towards Earth too, just sideways at the same rate, giving a stable orbit). The actual tree (a variety called the "Flower of Kent") still exists in the garden at Woolsthorpe Manor, supposedly grown from the original tree.
It took Newton another 20 years of careful work to turn his early insight into a full mathematical theory. In 1687 he finally published the Principia Mathematica, the book that contained his three laws and universal gravitation. The book changed science forever. Newton went on to become Master of the Royal Mint, President of the Royal Society and one of the most influential figures of his era. He was knighted by Queen Anne in 1705, the first scientist ever to receive that honour.
For more, see what is a force and momentum.