Classical Mechanics
Projectile motion, forces, energy, collisions, and rotational dynamics
- NewUniversity / research
Vortex Ring (Smoke Ring)
Self-propelling toroidal vortex shown as a 2D cross-section: counter-rotating Lamb–Oseen pair drifts at V_self ≈ Γ/(4πa).
- NewUniversity / research
Rayleigh–Taylor Instability
Heavy fluid above light: Fourier modes grow as exp(σt) with σ = √(A g k); mushrooming fingers reach down.
- NewUniversity / research
Faraday Waves
Vertical parametric drive of a thin liquid layer: Mathieu sub-harmonic instability locks stripes, squares or hexagons.
- NewUniversity / research
Airfoil Streamlines (Joukowski)
Potential flow over a Joukowski airfoil: stream-function bands with the Kutta condition fixing circulation.
- FeaturedSchool
Projectile Motion
Launch projectiles with adjustable angle, velocity, and gravity. Trace parabolic paths with real-time graphs.
- NewSchool
Trebuchet
Counterweight-driven beam: torque launches a projectile at a chosen release angle. Explore range vs masses and arm lengths.
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Chain Sliding Off Table
Uniform chain on a smooth edge: hanging weight pulls, friction on the tabletop resists. Watch when it slips and how acceleration grows wi…
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Block Stack & Friction
Pull the bottom block in a vertical stack: spring-like links with friction caps show who slips — compare with rigid-stack estimates.
- NewUniversity / research
Bicycle Stability (2D)
Side view: roll dynamics with fork trail and gyroscopic wheel torques — see speed, trail, and ω = v/R vs lean.
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Spring Pendulum
2D elastic pendulum: swing and spring stretch together — energy swaps between modes; try chaotic-looking presets.
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Bridge Resonance (1-D mode)
Damped modal oscillator with harmonic drive: sweep ω near √(k/m) — presets for cadence-like and low-ζ peaks.
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Rising Bubble (Archimedes)
Ideal-gas bubble expands as it rises (p = p_atm + ρgy); buoyancy vs weight + Stokes drag — depth and velocity graphs.
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Belt Drive & Slip
Two pulleys: tension difference limited by μ and wrap θ (e^{μθ}); load torque vs τ_max and simple slip on ω₂.
- School
Free Fall
Drop objects of different masses with optional air resistance. Prove Galileo right.
- School
Uniform vs Accelerated Motion
Compare constant velocity and accelerating objects side by side.
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Relative Motion
Boat crossing a river, plane in wind. Vector addition visualization.
- School
Circular Motion
Object on a string with centripetal acceleration and force vectors.
- FeaturedSchool
Force Diagram Builder
Place objects, add force vectors, see net force and resulting acceleration.
- NewKids
Newton's Cradle
Conservation of momentum and energy visualized with swinging balls.
- School
Inclined Plane
Adjust angle and friction. See force components and resulting motion.
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Inclined Plane: Work & η
W = F·s, friction and gravity work, ΔU, efficiency η = ΔU/W_F; slide-down preset.
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Friction Simulator
Static vs kinetic friction with adjustable coefficient.
- NewSchool
Slide to Stop
Initial velocity on a rough table: constant μ_k g decel, time and distance to rest.
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Atwood Machine
Two masses on a pulley. Adjust masses to see acceleration and tension.
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Elevator Physics
Person on a scale in an elevator. See apparent weight change.
- FeaturedSchool
Energy Conservation
Ball on a roller coaster track with real-time KE, PE, and total energy bars.
- NewSchool
1D Force Field
U(x) presets, F = −U′, bead on potential, phase (x,v) and E(t).
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1D Collisions
Elastic and inelastic collisions with momentum and energy tracking.
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2D Collisions
Billiard-ball style collisions with adjustable angles.
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Torque & Balance
Beam on a fulcrum. Place weights to balance or tip.
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Lever Classes
1st / 2nd / 3rd class: arms, τ about fulcrum, MA vs Torque & Balance.
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Blocks & Tackle
n supporting strands, same rope tension T, ideal MA = n, F = T.
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Simple Pendulum
Adjust length, mass, and gravity. Observe period and damping effects.
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Conical Pendulum
Steady cone: ω(θ,L), T and mg vectors, T_rev vs simple-pendulum T₀.
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Physical Pendulum (Rod)
Thin uniform rod: pivot along L, I and T(δ), equivalent length L_eq.
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Pendulum Collision
Two bobs: hit along normal, e elastic; θ¨ between hits vs 1D collisions.
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Yo-Yo Dynamics
Unwinding string: a = g/(1+I/mr²), T, α, optional friction torque τ.
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Satellite Yo-Yo Despin
L = const: ω_f = ω_0(I+2mr_i²)/(I+2mL²) as tethers pay out from r_i to L.
- NewKids
Rubber Sheet & Ball
Sheet height ∝ −Σm/r; ball rolls along −∇h — embedding metaphor, not GR.
- NewKids
Slinky Drop (Springs)
1D chain: release top anchor; bottom lags until stress wave — toy masses & k.
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Huygens Pendulum Sync
Two pendula + κ(θ₁−θ₂) on shared beam; phases drift toward lock.
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Ballistic Pendulum
Bullet hits block: embedded vs e; ω₀ = v/L, θ_max, energy graph.
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Center of Mass System
2–4 bodies or rod: R_cm, V_cm; explosion with ΣΔp = 0; |P| and |V_cm| graphs.
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Car on a Curve
Flat: v_max = √(μgR), F_c vs μmg. Banked ideal: tan θ = v²/(gR). Top view + wedge.
- NewUniversity / research
Quarter-Car Suspension
¼-vehicle vertical model: sprung vs unsprung masses, Kₛ, Cₛ, tire Kₜ, sinusoidal road — RK4 time histories.
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Capstan (Rope on Cylinder)
T₂ = T₁ e^{μφ}: μ, wrap angle φ, top view + T₂/T₁ vs φ graph.
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Spring Work (F–x)
F = kx graph, shaded W = area = ½kx²; U(x) curve vs Spring-Mass dynamics.
- NewFeaturedUniversity / research
Double Pendulum
Mesmerizing chaotic motion with path tracing.
- School
Spring-Mass System
Simple harmonic motion with adjustable spring constant and damping.
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Coupled Oscillators
Two masses, three springs: normal modes ωₛ, ωₐ and beats.
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Forced Oscillator
Driven damped harmonic oscillator: transients, resonance curve A(ω).
- Kids
Buoyancy Simulator
Drop objects in water. Float or sink based on density.
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Bernoulli Flow
Pipe narrows: speed up, pressure down. Continuity + Bernoulli.
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Hydraulic Press
Pascal: same pressure, large piston → large force. F₂ = F₁·A₂/A₁.
- NewUniversity / research
Rocket Propulsion
Variable mass: thrust ṁu, Tsiolkovsky Δv, vertical launch with gravity.
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Angular Momentum
Two masses on a rod: I = 2mr², change r or m and watch ω adjust to keep L constant.
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Rolling & Sliding Disk
No-slip v = ωR vs sliding: translational vs rotational KE, disk vs hoop inertia.
- NewUniversity / research
Gyroscope Precession
Gravity torque τ = mgd, spin L = Iω, steady precession Ω ≈ τ/L — schematic 3D view.
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Coriolis Effect
Puck on a rotating platform: curved path in the rotating frame vs straight line inertial.
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Wall Bounce
2D box: frictionless walls, restitution e, optional gravity. Trails and kinetic energy graph.
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Oblique Wall Impact
One tilted segment: e, angles to normal n, open boundaries vs closed Wall Bounce.
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Rutherford Scattering
Repulsive 1/r² orbit sketch vs impact parameter and energy.
- NewUniversity / research
Ideal Line Vortex
v_θ = Γ/(2πr) arrow field; circulation and potential flow cartoon.
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Forearm Lever (class 3)
Elbow fulcrum, load at hand, muscle moment arm — torque estimate.
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Communicating Vessels & Manometer
Hydrostatic balance, U-tube ΔP = ρgΔh, and inclined-tube vertical head.
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Simple Machines
Wedge, wheel & axle, and screw: ideal mechanical advantage vs geometry.
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Arch & Wedge Statics
Compressive thrust in a stone arch and wedge force resolution (schematic).
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Boids (Flocking)
Separation, alignment, cohesion on a torus; cursor as predator cue.
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Particle Life
Six types, pairwise matrix forces on a torus — clusters, worms, foam presets.
- NewUniversity / research
Poincaré Section (Double Pendulum)
(θ₁, ω₁) when sin θ₂ crosses 0 with ω₂>0; RK4, chaotic return map.
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Catenary Cable
Uniform chain between level anchors: y ∝ cosh(x/a); sag, arc length, tension directions.
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Magnus Effect (Ball)
Same v₀ and θ with vs without spin: toy a = (kωv_y, −g − kωv_x); range comparison.
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Fluid Surface (Accel / Spin)
Linear tank: tan α = a/g; rotating bucket: paraboloid sketch vs rpm.
- NewUniversity / research
Water Hammer (1D)
Linearized P,V waves; valve closes; Joukowsky ΔP ≈ ρaV hint.
- NewSchool
Foucault Pendulum (Sketch)
Ω_eff = Ω_E sin|λ| with time scale; top view rotating swing line.
- NewKids
Tippe Top (Schematic)
Offset COM, friction at rim, spin — qualitative flip when μ is high enough vs spin.
- NewUniversity / research
Kapitza Pendulum
Pivot shakes vertically: fast driving can stabilize the inverted equilibrium — parametric pumping in θ̈ + (g/L) sin θ ≈ (Aω²/L) cos(ωt) s…
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Rattleback (Celt)
Chiral hull couples spin and rocking in a toy ODE: one rotation sense reverses after growing wobble.
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Maxwell Wheel
Disk on a thin axle unwinds string: shared linear and rotational kinetic energy from falling potential, a ≈ g / (1 + I/(mr²)).
- NewUniversity / research
Brachistochrone Race
Beads race down a line, a circular arc, and a cycloid with v = √(2gy); the cycloid wins the descent-time minimum.
- NewSchool
Coupled Pendulum Chain
N pendula with neighbor springs in θ: watch traveling waves and reflections after a center kick.
- NewUniversity / research
Sliding Ladder
Frictionless wall and floor: θ̈ = −(3g/2L) cos θ; released from rest, wall contact is lost when sin θ = (2/3) sin θ₀.
- NewSchool
Angle of Repose
1D sandpile lattice: avalanches relax until slopes stay below μ = tan α — compare the green guide line.
- NewUniversity / research
Cart & Inverted Pendulum
Horizontal force on a cart with a hinged rod: coupled (M+m)ẍ and mL²θ̈ integrated for manual balancing.
- NewKids
Woodpecker Toy
Stick–slip sleeve on a rod: static hold, spring loading, then kinetic slip — a qualitative hop cycle.