# Conservação do Momento Angular

Visualização interativa da conservação L = Iω com plataforma giratória e momento de inércia ajustável

> Página canônica: https://elysiatools.com/pt/visualizations/angular-momentum-conservation

- **Categoria:** Physics

## Visão geral

Interactive visualization of angular momentum conservation with rotating platform experiment, figure skating analogy, and diver demonstration. Features the fundamental equations: Angular momentum L = I·ω (product of moment of inertia and angular velocity), Moment of inertia I = Σmr² (sum of mass times distance squared from axis), Conservation law I₁ω₁ = I₂ω₂ (when external torque τ_ext = 0, angular momentum remains constant), Torque τ = dL/dt (rate of change of angular momentum), Rotational kinetic energy E = ½Iω² = L²/(2I) (energy increases when I decreases, work done by internal forces). Real-time visualization includes: (1) Main Animation canvas with three scenarios - Rotating Platform (person with dumbbells on spinning platform, arm position r adjustable from 0.2-1.5m, platform radius 0.5-2.0m), Figure Skater (cylindrical body model with arm extension, body radius 0.15-0.6m, arm extension 0.0-1.0m), Diver (spherical body model for tucked/extended positions, body radius 0.2-1.0m). Each scenario shows 2D rotation with angular velocity ω display, person representation with body and arms, rotation axis visualization, motion trail showing path; (2) Angular Velocity Chart plotting ω vs time showing dramatic increase when arms contract, instantaneous ω values, comparison of different arm positions; (3) Moment of Inertia Chart plotting I vs time demonstrating I = mr² relationship, inverse correlation with angular velocity; (4) Angular Momentum Chart showing L = Iω = constant (horizontal line) proving conservation principle. Real-time value displays: Moment of Inertia I (kg·m²), Angular Velocity ω (rad/s), Angular Momentum L (kg·m²/s), Rotational Energy E (J). Interactive parameters: Mass m (30-120 kg), Initial angular velocity ω₀ (0.5-5.0 rad/s), Arm position r (0.2-1.5 m for platform), Body radius (0.15-0.6 m for skater), Arm extension (0.0-1.0 m for skater), Tuck position (0.2-1.0 m for diver), Platform radius (0.5-2.0 m), Animation speed (0.1-3x). Control buttons: Start, Pause, Reset, Contract Arms (r→0.2m), Extend Arms (r→1.5m), Auto Animate Arms (sinusoidal motion). Display options: toggle angular velocity vector visualization, motion trail, automatic arm animation. Educational content covers Angular momentum definition and conservation (L = Iω, vector quantity with direction along rotation axis, conserved when no external torque, fundamental law of physics), Moment of inertia concepts (I = Σmr² for discrete masses, I = ∫r²dm for continuous bodies, depends on mass distribution, farther mass = larger I), Rotating platform experiment (person with dumbbells, arms extended → large I → slow ω, arms contracted → small I → fast ω, dramatic speed-up clearly visible, L = Iω stays constant), Figure skating applications (skaters pull arms tight to spin faster, starting with extended arms for slow rotation, then rapid spin for jumps and camel spins, kinetic energy increase from muscle work, conservation in aerial maneuvers), Diver mechanics (tucked position reduces I for faster rotation, extended position slows rotation for water entry, angular momentum set at takeoff, cannot change in air, somersault and twist control), Everyday examples (playground merry-go-round, spinning chair with weights, cat's righting reflex, astronaut maneuvering, bicycle wheel demonstrations), Advanced applications (spacecraft attitude control with reaction wheels, neutron star spin-up during collapse, pulsar formation, planetary formation and angular momentum, helicopter rotor tail compensation). Multi-language support (zh, en, de, fr, es, pt, ru).

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