physics2u
Tier
⌕ Search ⌘K
physics2u.com/method.html
Why the pages look like this

The Method

Most physics explanations fail readers three ways: they hide the assumptions a result rests on, they never say where that result stops being true, and they skip the one step that was actually hard. Eight rules answer that — and every page on this site is built to obey them.

Rule 01

Every assumption, with its cost

An assumption is never stated on its own. Beside each one we name the consequence if you drop it — so you can see exactly what the result is buying with it.

Assumption.Small angle, sin θ ≈ θ.

Drop it and the pendulum stops being simple-harmonic; the period starts depending on amplitude.

Rule 02

Every result, its domain

A formula without a domain of validity is a trap. Each result carries the range of conditions where it holds — and a short list of where it breaks.

  • Fails at relativistic speeds, v → c.
  • Fails when the medium is dispersive.
  • Fails once quantum effects dominate the scale.
Rule 03

One operation per step

Derivations move one legal move at a time — differentiate, substitute, integrate — never two at once. The step that was actually hard gets its own line, not a "clearly it follows".

1
d/dt ( ∂L/∂q̇ ) − ∂L/∂q = 0
apply the Euler–Lagrange equation to a single coordinate B
Rule 04

Symbols before numbers

We carry symbols all the way to the answer and only substitute numbers at the very end. The algebra stays checkable, and a units check falls out for free.

T = 2π √(L ⁄ g)

Units check: √(m ÷ (m·s−2)) = √(s2) = s. Only then do we put in L = 1 m.

Rule 05

Three tiers, in place

The same page speaks at three depths at once: Tier 1 plain-language, Tier 2 the standard treatment, Tier 3 advanced rigour. They are layered into one document, not split across three.

The Tier toggle above works — flip it and this page rewrites: intuition-only, standard, or full rigour. Try it and watch the blocks appear and vanish.

Tier 3 · watch out

Tier 3 is where the caveats live — non-inertial frames, gauge choices, the terms everyone else quietly drops.

Rule 06

Written from the physics

Each derivation is authored independently from the physics itself — not paraphrased from a textbook, not stitched from search results. If a step is standard, we still re-derive it so the chain never has a gap you have to trust.

Authored independently

Two more rules — cite everything, and never round away a caveat — run silently through every page. The eight together are the whole reason the pages look the way they do.

See the rules applied — the curriculum → Read a derivation built this way →