Exploring Mechanics

An interactive, mathematics-first path through classical mechanics — from vectors and Newton's laws to gyroscopes, chaos, and counterintuitive puzzles. Each section below groups a set of related subtopics as tabs; pick a section to see what it covers.

0. Mathematical and Modeling Toolkit

Units, vectors, coordinate systems, reference frames, free-body diagrams.

5 subtopics

1. Kinematics: Describing Motion

Constant velocity, constant acceleration, free fall, projectile motion, relative motion.

5 subtopics

2. Newton's Laws and Forces

Inertia, F = ma, action-reaction, friction, inclined planes, tension.

6 subtopics

3. Work, Energy, and Power

Work-energy theorem, potential energy, conservation of energy, power, roller coasters.

7 subtopics

4. Momentum, Impulse, and Collisions

Momentum, impulse, collisions, center of mass, ballistic pendulum.

5 subtopics

5. Constraints and Simple Machines

Mechanical advantage, levers, pulleys, inclined planes/wedges, screws, gears.

6 subtopics

6. Circular Motion and Gravitation

Uniform circular motion, banked curves, vertical circles, gravitation, orbits.

5 subtopics

7. Rotational Mechanics and Rolling

Angular kinematics, torque, moment of inertia, rotational energy, rolling, angular momentum.

6 subtopics

8. Oscillations, Resonance, and Chaos

Simple harmonic motion, pendulums, damping, driven oscillations, resonance, coupled oscillators.

6 subtopics

9. Counterintuitive Mechanics Problems

Double cone uphill, spool paradox, rolling race, chain fountain, brachistochrone, and more.

12 subtopics

10. Real-World Capstone Simulations

Bowling, bicycles, roller coasters, bridge resonance, bows, catapults.

6 subtopics