Topic Brief: Equilibrium of a Particle Coplanar Forces

Provenance: written 2026-09-29. Sources read for this pass: research/veridian/WME01-verified-facts.md (§4 topics 2 and 5, §5, §9 lines 283–293 — the equilibrium-lesson audit entry); content/veridian/curriculum/wme01/equilibrium-of-a-particle-coplanar-forces.ts (header and citations, not its worked content); and, to confirm this document is genuinely additive rather than a restatement, the three existing WME01 technique-hub documents in full (codex-deep-dive-equilibrium-of-a-particle-coplanar-forces.md, forge-exam-technique-guide.md §1, signal-frequency-and-boundaries.md §1) plus content/veridian/question-bank/wme01.ts (grepped for "equilibrium/coplanar/Lami/resolv" — no hits). No new primary-source PDF was fetched this pass; every citation below traces to the facts bank, which itself names the real mark scheme, examiner report or question paper each claim came from.

#SIGNAL · Topic Master Brief — Equilibrium of a Particle Under Coplanar Forces

#Pearson Edexcel IAL Mechanics 1 (WME01/01), spec 5.1–5.2

Scope, narrowed on purpose: this brief tracks the bare form of this topic — a particle held in equilibrium by weight, normal reaction, tension or thrust, no friction involved — the same scope the topic's own lesson file uses. Friction-bearing equilibrium (spec 5.3, F ≤ μR) belongs to the sibling lesson (friction-equilibrium-and-motion-on-a-rough-plane.ts) and is named below only where a real series blends the two.

#1. Every real series this topic has been traced to

Seen in 4 of 17 series checked — 17 is the facts bank's own count of series with at least one genuine primary document reviewed (§5), not a claim that all 17 were individually screened for this one spec point. Of those 4, 2 show the bare form this topic's own lesson teaches (Jan 2022, Jan 2023); the other 2 show it blended into a friction/incline question. A fifth instance — Jun 2025 Q4 (7 marks, tagged 4.1/5.1: two forces resolved on a horizontal plane, then fed into Newton's second law) — is deliberately excluded from the count above: it exercises spec 5.1's resolving technique, not the equilibrium condition itself, so counting it would blur this brief's own scope line. The remaining 13 series in the archive were never tagged topic-by-topic for this spec point; their absence here means no document reviewed happened to record it, not that the topic was absent.

#2. Mark-tariff pattern

Two tariffs, one fully recovered, one only estimated from a table position:

• Bare form: 6 marks, split into two independently-scored 3-mark parts — the only instance with a full mark-scheme breakdown (Jan 2022 Q1).
• Blended-with-friction form: 11–12 marks, and in both fully-mapped recent series it landed at Q6 of a 7- or 8-question paper — a mid-paper position, not an opener and not the final question.

Two data points for each form. Not enough to fix either number as a rule, but enough to note the blended form runs roughly double the bare form's recovered tariff, and that both recent blended appearances shared the same question number.

#3. Recurring context or angle type

The one feature recurring across both series with any real method commentary for the bare form — Jan 2022 Q1 and Jan 2023 Q6, independently — is plural credited routes for the identical question: resolving twice, resolving along one unknown force, and Lami's theorem (or an equivalent triangle-of-forces/sine-and-cosine-rule method) are each named as full-credit alternatives in both series. That is the genuinely recurring pattern this evidence supports — not a specific angle or force type, since only one scenario has its actual numbers recovered at all (Jan 2022 Q1: a horizontal force opposed by two others at 30° and 60° to it).

#4. If this topic appears — what to expect

• Going only by the two most recently fully-mapped series (Jan 2025, Jun 2025), it is more likely to arrive blended into a friction/incline question than as a bare three-force problem — neither recent series shows the bare form.
• If it does appear bare, expect a small mark allocation per unknown (3 marks each, in the one recovered case) rather than one large combined question, and expect the mark scheme to credit more than one method equally — no route is worth more marks than another, only less time.
• Whichever form appears, the one specifically-verified trap for this exact spec point is a resolution equation missing a force's term — the topic lesson's own central trap (Jan 2022 Q1) and already covered in full there and in codex-deep-dive-equilibrium-of-a-particle-coplanar-forces.md §2; not repeated here.

#Sources and cross-references

• research/veridian/WME01-verified-facts.md §4 topics 2 and 5, §5, §9 (lines 283–293).
• forge-exam-technique-guide.md §1 — source of the Jan/Jun 2025 blended-form rows above.
• codex-deep-dive-equilibrium-of-a-particle-coplanar-forces.md — the fuller narrative treatment of the Jan 2022 Q1 anchor and this same frequency question (its own §6). This brief exists to give the same underlying facts a single-purpose, cite-by-series, table-first reference, which neither CODEX's teaching narrative nor SIGNAL's whole-paper table currently provides for this one topic.

#Genuinely unresolved

• Jan 2023 Q6's own marks were never recovered — the "6 marks" bare-form tariff above rests on one fully-recovered instance, not two.
• Whether the bare form appears in any of the 13 untagged series is genuinely unknown, not ruled out.