Foundations · Module 01
Before any law, the equipment: what a quantity is, what a unit is, and how to tell a real result from a rounding artefact. Skip this and every later module quietly punishes you.
By the end of this module
You can state any physical claim as a number with an honest error bar.
If I hand you a number, what has to be true for it to mean anything?
OpenStax
Free, rigorous, and the standard first-year text worldwide.
Caltech
Feynman's answer to 'if all knowledge were destroyed, what one sentence survives?'
Can I guess the form of a law before I derive it?
HyperPhysics (Georgia State)
Compact reference you will return to for years.
3Blue1Brown
Watch how far pure structure gets you before any calculation.
How wrong is my answer, and how do I say so honestly?
NIST
The document the world's metrology actually runs on.
How do I get within a factor of ten of an answer I have no data for?
MIT OCW 6.055J — The Art of Approximation
A whole MIT course on guessing well. Sanjoy Mahajan is the master of this.
What part of a description is the world, and what part is my choice of axes?
3Blue1Brown
The best visual intuition for vectors ever made. Watch chapters 1–3 now, the rest during Mathematics.
Check yourself
Every answer comes with the reasoning, not just a verdict. Getting one wrong and reading why is the point.
01A student reports a rod's length as 2.43671 m, measured with a ruler marked in millimetres. What is wrong?
02The period of a pendulum depends on length L and gravity g. By dimensions alone, T must be proportional to:
03Two quantities are added: 12.4 ± 0.3 and 7.61 ± 0.02. The uncertainty of the sum is closest to: