Exploring Mechanics
An interactive, mathematics-first path through classical mechanics, from Newton's laws to gyroscopes and chaos.
Mechanics has a reputation for being the physics you already know: things fall, things push back, things spin. Most of that intuition holds up for a block on a table. It stops holding up almost immediately once forces interact — a cone that rolls uphill, a pulley that halves your force and doubles your work, a spinning wheel that turns sideways instead of falling, a curve that gets a bead downhill faster than the straight line between two points.
Each section below is one stretch of that path, building from vectors and Newton’s laws up through energy, momentum, machines, rotation, oscillation, and a set of problems built specifically to break the intuition the earlier sections just built. Every page starts with a prediction before it shows you the answer.
0. The toolkit
Vectors, units, coordinate systems, reference frames, free-body diagrams — the vocabulary everything after this section assumes you already have.
Check out the toolkit →1. Kinematics
Position, velocity, and acceleration, described without yet asking what causes them — constant velocity, free fall, and projectile motion, up through relative motion between moving observers.
Check out kinematics →2. Newton's laws
Inertia, F = ma, and action-reaction pairs that don't cancel because they act on different objects — then friction, inclines, and connected objects as the first place the laws get genuinely hard to apply.
Check out Newton's laws →3. Work, energy, and power
A shortcut around messy force diagrams: track energy instead of force, and problems like roller coasters and pendulums stop needing calculus to solve.
Check out energy and power →4. Momentum, impulse, and collisions
What survives a collision that energy doesn't. A ballistic pendulum solves in two stages — momentum during the crash, energy after it — because no single conservation law covers the whole event.
Check out momentum and collisions →5. Constraints and simple machines
Levers, pulleys, screws, and gears all make the same trade: less force for more distance, never both. A movable pulley that halves your lifting force doubles how far you have to pull the rope — no exceptions.
Check out simple machines →6. Circular motion and gravitation
The force that keeps something moving in a circle points inward, not outward — "centrifugal force" is what it feels like from inside a rotating frame, not what's actually happening in an inertial one.
Check out circular motion →7. Rotational mechanics and rolling
Newton's laws again, but spinning: torque instead of force, moment of inertia instead of mass. A hoop, disk, and sphere released from the same height down the same ramp do not arrive together.
Check out rotation and rolling →8. Oscillations, resonance, and chaos
Simple harmonic motion repeats forever right up until damping or a second coupled pendulum enters the picture — then two nearly identical starting angles diverge into completely different futures.
Check out oscillations and chaos →9. Counterintuitive mechanics problems
A double cone that appears to roll uphill, a chain that fountains above the container it falls from, a straight line that loses a race to a curve. Predict the outcome before you read the resolution.
Check out the unintuitive problems →10. Real-world capstones
Bowling, bicycles, roller coasters, bridges, bows, and catapults, each built up in stages from the sections above — the payoff for having learned the individual pieces first.
Check out the capstones →This project is under active construction — each section currently outlines its subtopics, with full derivations and interactive simulations landing incrementally. Follow along on GitHub.