Mechanics · Module 1
The mathematics physics actually uses — vectors, coordinate systems, calculus and approximation, taught as a language rather than a toolkit.
Everything in this module exists to be used later. Nothing here is mechanics; it is what mechanics is written in. Eleven readings, fifty worked examples and a hundred and sixty problems, all free and all on this page.
Start here
Foundation 1 — The Language of Physics →
No prerequisites. It explains why physics reaches for mathematics at all, and ends with a short check on the six skills the rest of the module assumes.
The eleven Foundations
Read in order the first time. Each says at the top what it assumes.
1. The Language of Physics
Why equations describe rather than govern, and why every one carries conditions.
2. Scalars and Vectors
Why direction is not optional, and why a vector is not its components.
3. Coordinate Systems
Cartesian, polar, cylindrical and spherical — and the quadrant correction that costs marks every year.
4. Vector Addition and Resolution
Combining vectors and taking them apart, and why perpendicular components separate.
5. Dot Product
How much of one vector lies along another — and where work comes from.
6. Cross Product
Torque, area and the right-hand rule — which is an agreement, not a discovery.
7. Functions and Graphs
Reading a curve before computing on one. Slope is a rate; area is an accumulation.
8. Differentiation
Rates, equilibrium, the signature of simple harmonic motion, and where centripetal acceleration comes from.
9. Integration
Accumulation, and the constant that turns out to be an initial condition.
10. Approximations
The binomial and small-angle results, and why there is no exact treatment of anything.
11. Revision and Formula Sheet
Every formula in one place, with a source column, and twelve traps that cost marks.
Worked examples
Fifty examples, each with the full calculation and the question a physicist would ask around it. Read the first set after finishing the Foundations; the others as the topic comes up.
Module 1 — Worked Examples — one per Foundation, start here
Representation and Invariance — Foundations 2, 3, 4, 7
Dot and Cross Products — Foundations 5 and 6
Relative Motion and Equilibrium — Foundations 2 and 4
Reading Graphs — Foundation 7, the figures are the questions
Integration — Foundation 9, including a dx = v dv
Approximations — Foundation 10, and how Newton falls out of Einstein
Calculus in Rotating Frames — Foundations 3 and 8, the hardest page here
Putting It Together — all eleven at once
Problems
A hundred and sixty-two problems in five sets, none with answers. Work upward — each set assumes the one before.
JEE
Pre-Main Set — forty problems, no formulas required
Problem Set 1 — fourteen, Main level
Problem Set 2 — twelve, Advanced level
NEET
Recognition Set — forty MCQs, elimination rather than derivation
Timed Test — forty questions, forty-five minutes, negative marking
The page to keep open
Foundation 11 holds every formula from the module in one place, each marked with the Foundation it came from, plus the twelve errors that cost the most marks. It is written to be scanned rather than read.
Module 1 is complete. More is being written, and nothing is published until it is worth reading. If you find an error, or something that does not make sense, please tell me.