Interactive visual
01 · core
Balancing Act: Torque and Levers
force times lever arm decides which way it turns
A lever balances when m₁r₁ = m₂r₂. Torque is force times lever arm, and net torque over moment of inertia gives angular acceleration.
Physics
Mechanics
Forces, oscillation, orbits, torque, waves and fluids.
Interactive visual
02 · core
Buoyancy
the water pushes up with the weight of what you displace
Archimedes: a body is pushed up by the weight of fluid it displaces, so it floats with ρ_object/ρ_fluid of its volume under. Boats and crates in games.
Interactive visual
03 · common
Damped Pendulum
a sine-shaped pull back to the bottom, minus friction
A swinging weight pulled by sin θ: its period is only 2π√(L/g) for small swings, and damping decays the arc. Grapples, lamps and ropes in games.
Interactive visual
04 · common
Kepler's Laws
ellipses, equal areas, and T² ∝ a³
Orbits are ellipses with the star at one focus, sweep equal areas in equal times, and have T² ∝ a³. Place planets on rails exactly with Kepler's equation.
Interactive visual
05 · common
Projectile Data Lab
small launch errors become a spread of landing spots
Repeat a launch with a little speed error and the landings form a distribution. Mean, spread and why R ∝ v² shifts the average: the maths of weapon spread.
Interactive visual
06 · core
Projectile Motion
constant sideways speed, steadily changing vertical speed
Launch angle, speed and gravity fully determine a ballistic arc: x moves at constant speed while y accelerates downward.
Interactive visual
07 · common
Solar System: Two-Body Orbits
everything orbits the shared centre of mass
Two gravitating bodies circle their shared barycentre: radii split by mass, period set by total mass. Plus a stable n-body integrator for games.
Interactive visual
08 · core
Sound Waves
air molecules shuffle back and forth, the pattern travels
Sound is a longitudinal pressure wave: frequency sets pitch and wavelength, amplitude sets loudness. The physics behind 3D audio, delay and Doppler.
Interactive visual
09 · core
Spring-Mass Oscillator
pull back in proportion, bleed energy, push in rhythm
Hooke's law, damping and a periodic push: the forced oscillator behind springy cameras, wobbly UI and suspension, and why driving at ω₀ explodes.