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CodePhys Study Guide 📚

A physics course companion to the CodePhys engine. Each section teaches a physics topic from OpenStax College Physics 2e, then shows briefly how CodePhys lets you see it and where the relevant code lives — so you can poke the physics, not just read it.

This guide is about the physics. For the engine internals (rendering, UI, the simulation loop, the layered architecture) see docs/design/DESIGN.md. For the primary-literature sources behind each law, method, and constant, see docs/REFERENCES.md.

How to use this guide

Each chapter follows the same rhythm:

  1. 🎯 Learning objectives — what you should be able to do afterward.
  2. 📖 Textbook map — the matching OpenStax chapter(s).
  3. 🧠 Concepts & equations — the physics, with short derivations.
  4. 🔬 Try it — experiments to run in the app.
  5. ✅ Check yourself — questions with collapsible answers.

A short "in the code" note appears where it helps connect a formula to what you can run, but the focus is the physics.

Tip

Read a section, then open the app and reproduce its claims.

cmake --preset linux-gcc && cmake --build --preset linux-gcc
./build/linux-gcc/app/codephys

Curriculum map

# Section Physics OpenStax Ch.
01 Vectors, Units & SI scalars vs vectors, SI units, dimensional sense 1, 3.2
02 Kinematics & Projectile Motion displacement, velocity, acceleration, parabolic flight 2, 3
03 Newton's Laws & Acceleration force, mass, $F=ma$ 4, 5
04 Energy, Momentum & Conservation KE, PE, momentum, angular momentum, conservation 7, 8, 10
05 Simulating Motion Faithfully why simulated energy/orbits drift, and how to keep them honest 6–8 (applied)
06 Gravitation & Orbits inverse-square gravity, circular orbits, Kepler 6

The big ideas (one paragraph each)

  • Everything is SI. Metres, seconds, kilograms, radians — so a number in the sim can be compared directly to a textbook formula. → §01

  • Projectile motion is two 1D problems. Horizontal motion is constant-velocity; vertical motion is constant-acceleration under gravity. They share only a clock. → §02

  • Force sets acceleration. Newton's second law $\mathbf{a} = \mathbf{F}/m$ is the rule the whole engine runs on: know the force, get the acceleration, advance the motion. → §03

  • Conservation laws are the truth test. With no friction, mechanical energy is conserved; with no external force, momentum is; with no torque, angular momentum is. If the sim breaks one of these when it shouldn't, something is wrong. → §04

  • A simulation only approximates the physics. How you step time decides whether energy is conserved and whether an orbit stays an orbit. Watching a planet spiral away is a physics lesson about faithfulness, not a bug. → §05

  • Gravity is inverse-square and central. That single fact gives circular-orbit speed, Kepler's third law, and conserved angular momentum. → §06

Notation used throughout

Symbol Meaning SI unit
$\mathbf{r}$, $\mathbf{x}$ position m
$\mathbf{v}$ velocity m/s
$\mathbf{a}$ acceleration m/s²
$m$ mass kg
$\mathbf{F}$ force N (kg·m/s²)
$g$ gravitational field strength m/s²
$t$, $\Delta t$ (dt) time, timestep s
$\theta$ angle rad (deg in UI)
$E$, $K$, $U$ total / kinetic / potential energy J
$\mathbf{p}$, $L$ linear / angular momentum kg·m/s, kg·m²/s

Note

The app can only render ASCII, so on-screen you'll see T for $\theta$ and mu for $\mu$. This guide uses proper symbols.