Three short laws, published by Isaac Newton in 1687, explain how almost everything around you moves: a rolling ball, a braking car, a rocket, the Moon. This course takes them one at a time, with simulations to play with, missions to try and the real equations. Then it puts them to work on ramps and ropes, on crashes, and on the question Newton asked about the apple and the Moon.
Newton wrote his laws in Latin. Here is each one in plain words, as an equation, in everyday life, and in Newton’s own words with the English translation by Andrew Motte from 1729.
1The first law · inertia
An object stays at rest, or keeps moving in a straight line at a steady speed, unless a net force acts on it.
Fnet = 0 ⇔ v stays the same
A puck glides a long way on smooth ice. When a bus brakes, you lurch forward: your body keeps going.
Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impress’d thereon.
Lex I
2The second law · F = ma
The net force on an object equals its mass times its acceleration. Push harder and it speeds up faster; give it more mass and it speeds up more slowly.
Fnet = m a
An empty shopping cart is easy to get going. A full one needs a bigger push for the same start.
Mutationem motus proportionalem esse vi motrici impressæ, & fieri secundum lineam rectam qua vis illa imprimitur.
The alteration of motion is ever proportional to the motive force impress’d; and is made in the direction of the right line in which that force is impress’d.
Lex II
3The third law · action and reaction
When one object pushes or pulls on another, the second pushes or pulls back on the first, just as hard and in the opposite direction.
FA on B = −FB on A
When you walk, your foot pushes the ground backward, and the ground pushes you forward.
Actioni contrariam semper & æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales & in partes contrarias dirigi.
To every Action there is always opposed an equal Reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
Lex III
Latin: Isaac Newton, Philosophiæ Naturalis Principia Mathematica (London, 1687), “Axiomata, sive Leges Motus”. English: The Mathematical Principles of Natural Philosophy, translated by Andrew Motte (London, 1729). A “right line” is a straight line; by “motion” Newton meant mass times velocity, what we now call momentum.
The chapters
Each chapter starts with a simulation and a list of missions, then teaches the ideas behind it with worked examples, more small simulations and a short quiz. Take them in order, or jump in anywhere.
The whole course on one sheet. Bold letters in textbooks are vectors: quantities with a direction as well as a size, like force, velocity and acceleration.
Fnet = m a
Newton’s second law
Net force (N) = mass (kg) × acceleration (m/s²). 1 N = 1 kg·m/s².
Aristotle taught that things on Earth move only while something pushes them, and that heavier things fall faster. It fit everyday life, where friction stops everything, and it was taught for nearly two thousand years.
1632 and 1638
Galileo Galilei rolled balls down ramps and argued that a ball on a smooth, level surface would roll on forever, and that, without air, heavy and light things fall together.
1644
René Descartes, in his Principles of Philosophy, stated that a moving body keeps moving in a straight line unless something stops it.
1687
Isaac Newton published the Principia in London. Its three laws of motion, with his law of gravity, explained falling apples, tides, the Moon and the planets with the same few rules. Andrew Motte’s English translation followed in 1729.
1905 and 1915
Albert Einstein’s relativity showed where Newton’s laws need correcting: at speeds close to the speed of light, and where gravity is very strong.
Where Newton’s laws stop working
Near the speed of light (299,792,458 m/s), momentum is not just mv but γmv, where γ = 1 ÷ √(1 − v²/c²). Pushing harder can bring a particle ever closer to the speed of light, but never to it. In very strong gravity, near black holes and neutron stars, Einstein’s general relativity replaces Newton’s law of gravity. Even in the solar system the difference shows up, faintly: the orbit of Mercury, closest to the Sun, slowly turns in a way Newton’s gravity alone cannot explain, and the clocks in GPS satellites must be corrected for both kinds of relativity.
Why engineers still use Newton. For everything slower than a tiny fraction of the speed of light and far from extreme gravity, Newton’s answers are right to more decimal places than any measurement can check. Bridges, cars, elevators, airplanes, roller coasters and the paths of most spacecraft are designed with Newton’s laws. Try it:
At highway speed, Newton’s momentum is wrong by about 5 × 10⁻¹³ percent; even Voyager 1, coasting out of the solar system at 16.9 km/s, is off by less than a millionth of a percent. Only near light speed does the error grow large.