Work out what quantity a moving system is not allowed to lose, in enough detail to say in advance what a simulation of it must keep constant and to recognise the moment a calculation starts losing it

Motion and What Is Conserved

Mechanics taken from the other end. Instead of forces first, each lesson names the quantity that must not change, derives why, and watches a stepped calculation either hold it or quietly leak it away.

8 lessons, written and corrected before you arrived. Reading them here needs no account. The first reads the whole way through; the others open and then stop, because a page nobody owns cannot tell who is reading it. Starting the course gives you your own copy, where every idea has problems standing under it and you can ask about any sentence.

Start reading

01The Number That Does Not MoveA conserved quantity is a claim about every moment of a motion at once, which makes it the only thing a picture of that motion can be checked against.
02The Trade Between Two Halvesopening onlyConserved energy is rarely one thing sitting still. It is two things changing in step, and a turning point is where one of them has all of it.
03The Quantity That Survives a Collisionopening onlyEnergy can be lost to heat, so it is the wrong thing to hold a collision to. Momentum cannot be lost at all, and a calculation can keep it exactly.
04The Quantity That Turning Keepsopening onlyA third conserved combination notices circulation rather than travel. A force aimed at a point cannot change it, which is why a skater spins faster with her arms in.
05Three Axes, One of Them Treacherousopening onlyA freely spinning body keeps two quantities at once, and the two are not enough to keep it steady. About its middle axis it will always turn over.
06Ropes, Wheels and Forces That Do No Workopening onlyA rope ties two bodies into one number, and the pull in the rope does no work, so it never appears in the energy total and never has to be found.
07From One Particle to a Box of Gasopening onlyPressure is delivered momentum and temperature is average squared speed, so a gas needs no new physics. What it does need is counting, and counting is where time acquires a direction.
08The Quickest Way Downopening onlyEnergy conservation fixes the speed at each height whatever the path, which turns a question about a shape into a question about a total. The shape that wins is longer than the straight line.