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Sandbox Physics

Orbits · Oscillations · Chaos

Motion & dynamics

From a swinging pendulum to an orbit around a black hole.

115 experiments

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From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

6 Labs · about 100 min

  1. 01

    Observe

    Free Fall & Measuring Gravity

    Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth.

    14 min
  2. 02

    Compare

    Projectile Flight Designer

    Launch in vacuum first, then switch on drag and compare the range and apex with the vacuum reference.

    16 min
  3. 03

    Model

    Inclined Plane & Friction

    Change the slope and friction to find when the block can stay at rest, then predict whether it sticks or slides back after it stops.

    22 min
  4. 04

    Model

    One-Dimensional Collision Bench

    Move the restitution from elastic to sticking and check which quantity survives the collision: momentum or kinetic energy.

    20 min
  5. 05

    Model

    Mass–Spring Oscillator

    Change the mass, stiffness and release distance, then measure eight periods to find which one actually sets the period.

    18 min
  6. 06

    Transfer

    How Orbits Take Shape

    Raise the launch speed from circular-orbit speed toward escape speed, and compare the recorded path with the predicted conic section.

    10 min

Browse the collection

115 experiments

  1. Motion & dynamics

    Supernova Distance and Cosmic Expansion

    How do distant supernovae reveal the history of cosmic expansion?

    15 min

  2. Motion & dynamics

    Inside a Star in Hydrostatic Balance

    What holds a star up against its own gravity?

    15 min

  3. Motion & dynamics

    Pulsar Timing and Orbital Decay

    How can pulse arrival times reveal an orbit that slowly shrinks?

    15 min

  4. Motion & dynamics

    Conical Pendulum

    Why does a wider cone complete a turn sooner?

    10 min

  5. Motion & dynamics

    Centrifugal Governor

    Why does the sleeve rise as the spindle speeds up?

    10 min

  6. Motion & dynamics

    Pantograph Drawing Copier

    How can four bars copy a drawing at a different size?

    12 min

  7. Motion & dynamics

    Scissor Lift & Virtual Work

    Why is a scissor lift hardest to raise near the ground?

    12 min

  8. Motion & dynamics

    Tusi Couple & Inner Rolling Tracer

    Can two circles draw an exact straight line?

    12 min

  9. Motion & dynamics

    Outer Rolling Tracer

    Why does the pen stop at a cusp while its center moves?

    12 min

  10. Motion & dynamics

    Cam Motion Designer

    Can a follower stop while the cam keeps turning?

    12 min

  11. Motion & dynamics

    Crank-Shaper Quick Return

    Why does a steady motor give the ram a fast return?

    12 min

  12. Motion & dynamics

    Peaucellier Inversor

    How can hinged bars draw a straight line without a guide?

    12 min

  13. Motion & dynamics

    Trammel of Archimedes

    On a trammel of Archimedes, where should the pen sit to draw a circle?

    12 min

  14. Motion & dynamics

    Universal Joint

    Why does a universal joint set at an angle make the output speed up and slow down twice each turn?

    15 min

  15. Motion & dynamics

    Oldham Coupling

    Can two offset shafts turn at exactly the same speed while the middle disc slides?

    15 min

  16. Motion & dynamics

    Geneva Drive

    How can a turning input make the output wait?

    15 min

  17. Motion & dynamics

    Scotch Yoke

    How does a slot turn a circle into a sine wave?

    15 min

  18. Motion & dynamics

    Four-Bar Linkage

    Which link lengths let a four-bar linkage's input crank turn all the way around?

    20 min

  19. Motion & dynamics

    Slider-Crank Workshop

    Why does a crank turning at steady speed move the slider unevenly?

    20 min

  20. Motion & dynamics

    Cart-Pole Balance

    Can a cart's motor catch a falling pole and then bring the cart back to its start?

    20 min

  21. Motion & dynamics

    Reaction-Wheel Balance

    How can spinning up a wheel keep a rod upright?

    20 min

  22. Motion & dynamics

    Rolling Wheel & Geometric Phase

    If a wheel's heading and roll angle both return to their start, is the wheel back where it began?

    20 min

  23. Motion & dynamics

    Chaplygin Sleigh

    Can a sleigh on a knife edge slow its turning without losing any energy?

    20 min

  24. Motion & dynamics

    Drum Modes & Strike Position

    Why does striking a drum in a different spot change its vibration but not its frequencies?

    20 min

  25. Motion & dynamics

    Chladni Plate Resonance

    Does driving a plate at one of its resonant frequencies always make that pattern vibrate?

    20 min

  26. Motion & dynamics

    Tidal Field Explorer

    Why do tides stretch both the near side and the far side?

    15 min

  27. Motion & dynamics

    Tidal Locking & Libration

    Why must a moon keep spinning to show its planet the same face?

    20 min

  28. Motion & dynamics

    Gear Train & Idler

    Does an extra gear change speed or direction?

    15 min

  29. Motion & dynamics

    Planetary Gears & Two Inputs

    In a planetary gear set, why does holding a different part change how the others turn?

    20 min

  30. Motion & dynamics

    Swinging Spring & Internal Resonance

    Can a bounce lend its energy to a swing?

    20 min

  31. Motion & dynamics

    Tuned-Mass Damper Design

    Can a small tuned mass keep a structure from shaking hard at resonance?

    28 min

  32. Motion & dynamics

    Parametric Resonance Playground

    Can changing stiffness add energy without an applied drive force?

    28 min

  33. Motion & dynamics

    Satellite Attitude & Gravity Gradient

    What can a long boom and a momentum wheel each do to keep a satellite pointed?

    30 min

  34. Motion & dynamics

    Tennis-Racket Theorem

    Why does a free object spinning about its middle axis keep flipping over?

    30 min

  35. Motion & dynamics

    Gyroscope Precession Bench

    Why does a spinning wheel precess instead of simply falling?

    30 min

  36. Motion & dynamics

    Spinning Top: Precession & Nutation

    When does a nearly upright spinning top stay upright?

    30 min

  37. Motion & dynamics

    Coriolis Turntable

    Why does a puck sliding freely on a turntable seem to curve when nothing pushes it sideways?

    30 min

  38. Motion & dynamics

    Foucault Pendulum & Earth Rotation

    Why does a Foucault pendulum's length change its swing period but not how fast its swing plane turns?

    30 min

  39. Motion & dynamics

    Chaotic Billiards Arena

    Can geometry alone create chaos?

    35 min

  40. Motion & dynamics

    Kicked Rotor & KAM Transition

    Does keeping phase-space area fixed protect a kicked rotor from chaos?

    35 min

  41. Motion & dynamics

    Principle of Stationary Action

    Must the physical path have the smallest action?

    30 min

  42. Motion & dynamics

    Hamiltonian Phase Space & Integrators

    When a computer simulates an orbit, can a small energy error hide a wrong trajectory?

    30 min

  43. Motion & dynamics

    Binary-Star Mass Laboratory

    Can motion weigh stars without knowing the viewing angle?

    30 min

  44. Motion & dynamics

    Gravity-Assist Mission Designer

    How can a flyby change speed without an engine burn?

    30 min

  45. Motion & dynamics

    Hohmann Transfer Planner

    Can two burns change an orbit and meet a moving target?

    30 min

  46. Motion & dynamics

    Orbital Rendezvous in the Hill Frame

    Does reaching the target also mean matching its velocity?

    30 min

  47. Motion & dynamics

    One-Dimensional Potential Landscape

    Can you predict a particle's motion just from a graph of its potential energy?

    25 min

  48. Motion & dynamics

    Double-Well, Barrier & Separatrix Lab

    How does a barrier between two wells change the way a particle moves?

    30 min

  49. Motion & dynamics

    Mechanical Lattice & Dispersion

    How does a wave packet travel when its crests and its envelope move at different speeds?

    30 min

  50. Motion & dynamics

    FPUT Recurrence Laboratory

    In a chain of masses and springs, can energy spread among the vibration modes and later return?

    30 min

  51. Motion & dynamics

    Granular Impact Chain Designer

    For the same impact energy, can grading the bead masses in a chain lower the peak force on the wall?

    30 min

  52. Motion & dynamics

    Duffing Oscillator Laboratory

    Why can the same forcing frequency produce different responses?

    28 min

  53. Motion & dynamics

    Finite-Amplitude Pendulum

    Does a bigger swing change a pendulum's period?

    22 min

  54. Motion & dynamics

    Bead on a Rotating Hoop

    Where does a bead on a spinning hoop settle?

    25 min

  55. Motion & dynamics

    Driven Pendulum & Poincaré Section

    Does a driven pendulum repeat itself if you check it once every drive cycle?

    30 min

  56. Motion & dynamics

    Inclined Plane & Friction

    At zero speed, will the block stick or reverse?

    22 min

  57. Motion & dynamics

    Accelerating Wedge & Sliding Block

    Can a frictionless normal force transfer energy?

    22 min

  58. Motion & dynamics

    Atwood Machine

    In an Atwood machine, why are the rope tensions on the two sides unequal?

    22 min

  59. Motion & dynamics

    Pulley Network & Mechanical Advantage

    When a pulley system lets you pull with less force, where does the saved force go?

    22 min

  60. Motion & dynamics

    Catenary & Suspension Cable

    Is every hanging cable a parabola?

    20 min

  61. Motion & dynamics

    Center of Mass & Tipping

    When an object could tip over any of several edges, which one goes first?

    20 min

  62. Motion & dynamics

    Lagrange Points & Three-Body Channels

    If a probe has enough energy to cross from one body's region to the other's, will it actually cross?

    25 min

  63. Motion & dynamics

    N-Body Star Cluster

    What happens after a cold cloud collapses?

    25 min

  64. Motion & dynamics

    Free-Body Diagram Builder

    Which forces belong in an object's free-body diagram?

    20 min

  65. Motion & dynamics

    Stacked Blocks & Friction

    When you push one of two stacked blocks, which contact slips first?

    20 min

  66. Motion & dynamics

    Spring Launcher

    Will the ball actually leave the spring?

    15 min

  67. Motion & dynamics

    Bouncing Ball & Restitution

    Where does the missing height go?

    15 min

  68. Motion & dynamics

    Galilean Frame Switcher

    Which quantities of motion change when the observer changes?

    25 min

  69. Motion & dynamics

    Center-of-Momentum Frame Lab

    Can total momentum vanish while both bodies keep moving?

    25 min

  70. Motion & dynamics

    Elevator Scale & Apparent Weight

    When does a scale stop measuring your weight?

    25 min

  71. Motion & dynamics

    Terminal Fall & Drag Laws

    Can two falling masses reveal the drag law?

    25 min

  72. Motion & dynamics

    Motion Graph Studio

    Can one drawn curve determine the whole motion?

    25 min

  73. Motion & dynamics

    Motion Measurement & Numerical Differentiation

    Do more frames always give better acceleration?

    25 min

  74. Motion & dynamics

    Work–Energy Graph Studio

    Can the area under a force-position graph predict how an object moves?

    25 min

  75. Motion & dynamics

    Conservative Forces & Path Dependence

    Does a force do the same work along any path between the same two points?

    25 min

  76. Motion & dynamics

    Curvature & Frenet Track Designer

    How do the bends in a track and the speed along it set the normal acceleration?

    25 min

  77. Motion & dynamics

    Polar-Coordinate Kinematics

    How do you find the velocity and acceleration of a point on an arm that stretches while it turns?

    25 min

  78. Motion & dynamics

    Crash Pulse & Impulse Engineering

    If the same impulse stops an object, why does it matter when the force acts?

    25 min

  79. Motion & dynamics

    Braking Distance & Power Limits

    How do reaction time, tyre grip and brake power each decide how far a car goes before it stops?

    25 min

  80. Motion & dynamics

    Gravity Field & Shell Theorem

    Inside a hollow shell, where does the shell's gravity go?

    25 min

  81. Motion & dynamics

    Virial Theorem Observatory

    When does the virial theorem actually hold?

    25 min

  82. Motion & dynamics

    Roller-Coaster Energy Designer

    Can a roller-coaster car with enough energy to reach the top of a loop still leave the track?

    25 min

  83. Motion & dynamics

    Cycloid Challenge: Fastest & Isochronous

    Which curve lets a bead slide down fastest and also makes beads from any height arrive together?

    25 min

  84. Motion & dynamics

    Column Buckling & Imperfection

    Does a loaded column fail first by buckling or by its material yielding?

    30 min

  85. Motion & dynamics

    Stress–Strain Material Tester

    What is left in a material after you load it and then take the load off?

    30 min

  86. Motion & dynamics

    Buoyancy & Metacentric Stability

    Can a floating hull still overturn?

    30 min

  87. Motion & dynamics

    Shallow-Water Waves & Dam Break

    Does a dam-break flood front move at the speed of small water waves?

    30 min

  88. Motion & dynamics

    Couette–Poiseuille Viscous Flow

    Can a moving wall reverse a pressure-driven stream?

    25 min

  89. Motion & dynamics

    Surface Tension & Capillary Laboratory

    Can the height a liquid climbs in a thin tube tell surface tension apart from wetting?

    25 min

  90. Motion & dynamics

    Continuity & Bernoulli Flow Bench

    Where does the pressure go when liquid flows through a narrow part of a pipe?

    25 min

  91. Motion & dynamics

    Siphon, Pressure Limit & Cavitation

    How high can a primed siphon lift the liquid?

    25 min

  92. Motion & dynamics

    Hydrostatics & Hydraulic Press

    Does a hydraulic press give out more work as well as more force?

    20 min

  93. Motion & dynamics

    Draining Tank & Torricelli Law

    Can a draining tank's falling water level show how far the outflow falls short of the ideal?

    20 min

  94. Motion & dynamics

    Truss Bridge Force Explorer

    What is the least material a truss bridge needs to carry a load anywhere on its deck?

    25 min

  95. Motion & dynamics

    Beam Bending Laboratory

    Can measured bending reveal material stiffness?

    25 min

  96. Motion & dynamics

    Balance Beam & Torque Puzzle

    Can the smallest counterweight balance a loaded beam?

    20 min

  97. Motion & dynamics

    Capstan & Belt Friction

    With a rope wrapped around a drum, how little force can hold a heavy load?

    20 min

  98. Motion & dynamics

    Angular-Momentum Skater

    Can angular momentum stay fixed while kinetic energy increases?

    22 min

  99. Motion & dynamics

    Moment-of-Inertia Designer

    Which distances matter to rotational inertia?

    22 min

  100. Motion & dynamics

    Rolling Race Laboratory

    Does a solid sphere always win a race down a slope?

    22 min

  101. Motion & dynamics

    Yo-Yo & Spool Direction Puzzle

    Does a spool always roll the way you pull its string?

    22 min

  102. Motion & dynamics

    One-Dimensional Collision Bench

    What survives an inelastic collision?

    20 min

  103. Motion & dynamics

    Two-Dimensional Collision Table

    What sets the scattering angle in a two-dimensional collision?

    22 min

  104. Motion & dynamics

    Ballistic Pendulum Lab

    Can you work out a projectile's speed from how high the pendulum swings?

    24 min

  105. Motion & dynamics

    Double Pendulum & Chaos

    How long do two nearly identical releases of a double pendulum follow the same path?

    8 min

  106. Motion & dynamics

    How Orbits Take Shape

    How can one force law draw three different conic sections?

    10 min

  107. Motion & dynamics

    How Coupled Springs Move Together

    Can one bead's swing grow and fade while the energy in every normal mode stays fixed?

    10 min

  108. Motion & dynamics

    Binary Neutron Star Merger

    What happens when two neutron stars spiral together and merge?

    14 min

  109. Motion & dynamics

    How a Black Hole Bends Light

    Why can one thin accretion disk appear both above and below the black-hole shadow?

    12 min

  110. Motion & dynamics

    The Three-Body Dance

    Why does one extra body remove the general orbit formula?

    12 min

  111. Motion & dynamics

    Mass–Spring Oscillator

    What sets the period of a mass bouncing on a spring?

    18 min

  112. Motion & dynamics

    Damped Oscillations & Ringdown

    When can the peaks of a filmed oscillation give you its damping and stiffness?

    18 min

  113. Motion & dynamics

    Driven Resonance & Phase Lag

    Do a driven oscillator's largest swing and largest power intake happen at the same frequency?

    18 min

  114. Motion & dynamics

    Free Fall & Measuring Gravity

    Can a noisy camera and a coarse photogate timer measure gravity accurately?

    14 min

  115. Motion & dynamics

    Projectile Flight Designer

    How do you aim a launch to hit a target through drag and crosswind?

    16 min

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