This is a working draft for Leslie's review. The dependency edges below are a first pass — the diagram and the prerequisite table are the parts to check hardest, since they drive hold-vs-advance decisions.
The course map shows the eight units as a spine — kinematics first, fluids last. But the real prerequisite structure isn't a straight line: it's a directed graph. Physics is more strictly cumulative than most subjects — dynamics needs kinematics; energy, momentum, and torque all need dynamics; simple harmonic motion needs both energy and dynamics. A weak concept early doesn't just lower one grade, it cascades into everything downstream that needs it. This page is the map a guide uses to find the concept that's actually blocking a stuck student.
An arrow means the later unit builds on the earlier one. The course runs left to right: Kinematics and Dynamics first, then a branch through Circular Motion and Energy that converges at Momentum, a second branch through Simple Harmonic Motion and Torque, and a final convergence at Fluids. The two convergence points — Momentum (05) and Fluids (08) — are where one soft earlier unit quietly weakens several later ones. The exact prerequisites are in the table below.
Prerequisite gating
A unit unlocks when its prerequisites are mastered — demonstrated, not merely seen. "Covered in class" is not the gate; a cleared rubric is. The difference matters most at the cascade points, where a soft prerequisite quietly breaks two or three later units.
| Unit | Must have mastered first |
|---|---|
| 01 Kinematics & Motion | — (entry point) |
| 02 Dynamics & Newton's Laws | 01 (velocity & acceleration underpin every force analysis) |
| 03 Circular Motion & Gravitation | 02 (centripetal force is a Newton's-law application) |
| 04 Energy & Work | 02 (work is a force acting through a distance) |
| 05 Momentum & Collisions | 02 (impulse is force applied over time) |
| 06 Simple Harmonic Motion | 02 (a restoring force drives the oscillation) + 04 (energy trades between kinetic & potential) |
| 07 Torque & Rotational Motion | 02 (torque is the rotational form of Newton's second law) |
| 08 Fluids & Pressure | 02 (pressure is force per unit area) + 04 (Bernoulli is energy conservation in a flow) |
Gap-cascade diagnosis
When a student stalls late, the visible symptom is rarely the real problem — the broken concept is usually upstream. Trace the arrows backward. Common cascades:
| Late symptom | Upstream concept to check first |
|---|---|
| Bernoulli and pressure problems fall apart (Unit 08) | Energy & work from Unit 04 — Bernoulli is energy conservation in a moving fluid. |
| Oscillation period and energy won't resolve (Unit 06) | Newton's second law from Unit 02 — the restoring force sets the whole motion. |
| Collision outcomes come out wrong (Unit 05) | Force analysis from Unit 02 — impulse is force applied over time, not a memorized formula. |
| Centripetal and orbit problems stall (Unit 03) | Free-body reasoning from Unit 02 — centripetal force is just the net force pointed inward. |
Using the graph to plan a re-attempt
The graph turns a "not yet" into a targeted re-attempt instead of a whole-unit re-teach. When a student fails a downstream demonstration:
- Trace backward to the upstream node the symptom points to.
- Re-attempt the upstream concept first — close the gap at its source, not where it surfaced.
- Then re-run the downstream demonstration. Often it passes without any re-teaching of the downstream unit at all, because the cascade is resolved.
This is also where the integration guide matters: some physics concepts depend on an applied-math idea — trigonometry for resolving force vectors, proportional reasoning for scaling relationships — from another spoke. When the upstream physics node looks solid but the student still stalls, check the cross-disciplinary dependency before re-teaching the physics.