Use the hub when you want a concrete next move instead of open browsing. Filters stay on canonical topics, tracks, depth, and progress while the visible labels localize cleanly.
Starting from Calm start, make the oscillator complete a shorter cycle without turning it into a wider swing. Keep the displacement graph open so the timing change stays visible.
Simple Harmonic Motion
Not started on this browser yet.
Use compare mode to keep a calm baseline in Setup A and make Setup B cycle faster while both setups keep about the same swing size.
Simple Harmonic Motion
Not started on this browser yet.
Guided challenge paths
These paths keep the concept order and challenge sequencing together without inventing a separate challenge graph.
Start with vector components, move into projectile paths, and then use circular motion to understand how velocity can keep changing direction.
0
Solved
0
Started
8
To try
Short-period force band is the next best challenge from Uniform Circular Motion.
Start with torque as the turning effect of force, use centre of mass and support region for static balance, then carry the same rotational language into moment of inertia, rolling motion, and angular momentum.
0
Solved
0
Started
15
To try
Zero turn at the handle is the next best challenge from Torque.
Start with one source mass creating a field and potential well, then use that same gravity model to explain circular speed, orbital periods, and the escape threshold.
0
Solved
0
Started
12
To try
Keep the heavier source circular is the next best challenge from Circular Orbits and Orbital Speed.
Build from one clean oscillator to energy exchange and then to driven resonance, so the same system grows without changing its core ideas.
0
Solved
0
Started
6
To try
Short-period match is the next best challenge from Simple Harmonic Motion.
Start with pressure in a resting fluid, then carry that same branch through continuity, Bernoulli, buoyancy, and drag-limited motion.
0
Solved
0
Started
10
To try
Build the 27 kPa throat is the next best challenge from Bernoulli's Principle.
Use oscillation as the entry point, lock down wave speed and wavelength, carry that into longitudinal sound and pitch-versus-loudness cues, add beats as the nearby-frequency superposition bridge, then move into Doppler shifts, interference, standing-wave patterns, and open-vs-closed air-column resonance without losing the live connection between motion and graph.
0
Solved
0
Started
15
To try
Short-period match is the next best challenge from Simple Harmonic Motion.
Start with temperature-versus-internal-energy bookkeeping, reuse that particle story for gas pressure, then follow energy transfer into heating curves and phase-change shelves.
0
Solved
0
Started
8
To try
Same contrast, slower loss is the next best challenge from Heat Transfer.
Start with source charges and voltage, then carry that same circuit story into current, power, branch behavior, and equivalent resistance.
0
Solved
0
Started
7
To try
Build the upward field is the next best challenge from Electric Fields.
Start with current-made magnetic fields, turn changing flux into induced emf with Faraday and Lenz, and then reuse that same field direction story to explain magnetic force on charges and currents.
0
Solved
0
Started
6
To try
High flux, zero emf is the next best challenge from Faraday's Law and Lenz's Law.
Stay on the sound branch long enough that longitudinal motion, pitch-versus-loudness cues, beats, Doppler shifts, and open-vs-closed air-column resonance feel like one acoustics path instead of isolated pages.
0
Solved
0
Started
9
To try
Tune slow pulses is the next best challenge from Beats.
Follow the bounded wave-optics branch from polarization into diffraction, double-slit interference, color-dependent refraction, and imaging limits so the newer optics pages read like one compact path instead of isolated stops.
0
Solved
0
Started
10
To try
Set a half-power case is the next best challenge from Polarization.
Follow the bounded modern-physics branch from threshold emission into line spectra, matter waves, the Bohr hydrogen model, and half-life so the new concept set reads like one path instead of five isolated pages.
0
Solved
0
Started
10
To try
Find the stopping point is the next best challenge from Photoelectric Effect.
Keep the first math path compact: read parent-curve moves first, then rational asymptotes and domain breaks, then exponential growth and decay, local slope, visible limit behavior, and finally accumulation so change stays graph-first all the way through.
0
Solved
0
Started
6
To try
Reflect and land the vertex is the next best challenge from Graph Transformations.
Start with complex numbers as points on one plane, turn that plane into unit-circle and polar-coordinate geometry, deepen that same bench into trig identities and inverse-angle reasoning, then carry the coordinate language into motion traced from x(t) and y(t).
0
Solved
0
Started
6
To try
Rotate onto the positive imaginary axis is the next best challenge from Complex Numbers on the Plane.
Start with vectors as geometric objects on a 2D plane, then carry the same component language into the existing motion-facing vectors bench.
0
Solved
0
Started
3
To try
Equal components is the next best challenge from Vectors and Components.
Start with successful collisions setting reaction rate, then reuse the same chemistry language inside a reversible system that re-balances after a disturbance.
0
Solved
0
Started
2
To try
More success, not just more hits is the next best challenge from Reaction Rate / Collision Theory.
Start with one visible reaction recipe, use the lower batch cap to identify the limiting reagent, and then compare actual output with the same theoretical marker.
0
Solved
0
Started
3
To try
Build the matched 3:2 run is the next best challenge from Stoichiometric Ratios and Recipe Batches.
Start with concentration in one beaker, add solubility limits and saturation, then reuse that same solution language to read pH, buffers, and neutralization.
0
Solved
0
Started
4
To try
Dilute without losing solute is the next best challenge from Concentration and Dilution.
Start with visible list work, reuse that search language for binary search, and then carry the branch into one live graph bench for adjacency, BFS, DFS, and visited-state behavior.
0
Solved
0
Started
2
To try
Use insertion where it pays off is the next best challenge from Sorting and Algorithmic Trade-offs.
Challenge browser
Filters stay on canonical content ids while the visible copy localizes through the shared message and content layers.
Topics
More filters
Track, depth, and progress filters stay optional.
Starter paths
Depth
Progress
Starting from Calm start, make the oscillator complete a shorter cycle without turning it into a wider swing. Keep the displacement graph open so the timing change stays visible.
Simple Harmonic Motion
See one repeating system from displacement to acceleration and back again, with the math tied directly to the motion on screen.
Not started on this browser yet.
Use compare mode to keep a calm baseline in Setup A and make Setup B cycle faster while both setups keep about the same swing size.
Simple Harmonic Motion
See one repeating system from displacement to acceleration and back again, with the math tied directly to the motion on screen.
Not started on this browser yet.
Starting from Mixed energy, pause at a moment when kinetic and potential energy are nearly equal. Keep the energy graph visible so the balance is honest.
Oscillation Energy
Watch kinetic and potential energy trade places in simple harmonic motion while the total stays fixed by amplitude and spring stiffness.
Not started on this browser yet.
From the mixed-energy baseline, raise the stored energy to about $5\,\mathrm{J}$ without making the oscillator heavier than about $1.2\,\mathrm{kg}$.
Oscillation Energy
Watch kinetic and potential energy trade places in simple harmonic motion while the total stays fixed by amplitude and spring stiffness.
Not started on this browser yet.
Starting near unison, tune the source pair until the envelope pulses at about $0.2\,\mathrm{Hz}$ while the source amplitude stays near the baseline.
Beats
Superpose two nearby sound frequencies, watch the fast carrier sit inside a slower envelope, and connect beat rate to the frequency difference on one compact bench.
Not started on this browser yet.
Enter compare mode and make Setup B keep the same beat frequency as Setup A while clearly lowering the average carrier frequency.
Beats
Superpose two nearby sound frequencies, watch the fast carrier sit inside a slower envelope, and connect beat rate to the frequency difference on one compact bench.
Not started on this browser yet.
Keep the emitted tone near 1.1 Hz and tune the live setup so the observer clearly hears a higher pitch on the moving-source bench.
Doppler Effect
Watch a moving sound source compress wavefronts ahead and stretch them behind, then see how source motion and observer motion combine to change the heard pitch on one bounded classical bench.
Not started on this browser yet.
Enter compare mode and make Setup A hear a lower pitch than emitted while Setup B hears a higher pitch, with both sources keeping the same emitted frequency.
Doppler Effect
Watch a moving sound source compress wavefronts ahead and stretch them behind, then see how source motion and observer motion combine to change the heard pitch on one bounded classical bench.
Not started on this browser yet.
Enter compare mode and make Setup B louder than Setup A while keeping the pitch the same.
Pitch, Frequency, and Loudness / Intensity
Keep one compact sound bench while separating pitch from frequency, loudness from amplitude and an amplitude-squared intensity cue, and probe delay from the source sound itself.
Not started on this browser yet.
Starting from Baseline, move the probe until it sits inside a strong compression while the probe-pressure graph and compression overlay stay visible.
Sound Waves and Longitudinal Motion
See sound as a longitudinal wave by keeping parcel motion, compression and rarefaction, probe timing, and energy transfer tied to one compact medium-first bench.
Not started on this browser yet.
Enter compare mode and keep Setup B one full wavelength farther downstream than Setup A so both probes share the same phase relation but Setup B arrives one cycle later.
Sound Waves and Longitudinal Motion
See sound as a longitudinal wave by keeping parcel motion, compression and rarefaction, probe timing, and energy transfer tied to one compact medium-first bench.
Not started on this browser yet.
Starting from Center bright, move the probe onto a dark region where the screen intensity almost vanishes.
Wave Interference
Superpose two coherent sources, trace their path difference to phase difference, and watch bright and dark regions emerge on the same live screen.
Not started on this browser yet.
From Center bright, pause at a moment when the resultant amplitude is still large but the instantaneous probe displacement has crossed through zero.
Wave Interference
Superpose two coherent sources, trace their path difference to phase difference, and watch bright and dark regions emerge on the same live screen.
Not started on this browser yet.
Starting from the third harmonic, move the probe onto a node so the local oscillation envelope collapses almost to zero.
Standing Waves
Track fixed nodes, moving antinodes, and harmonic mode shapes on one live string while the same probe trace shows the underlying oscillation in time.
Not started on this browser yet.
From the fundamental mode, keep the probe at the center antinode and pause right as that antinode crosses through zero displacement.
Standing Waves
Track fixed nodes, moving antinodes, and harmonic mode shapes on one live string while the same probe trace shows the underlying oscillation in time.
Not started on this browser yet.
Starting from the closed-pipe third harmonic, move the probe onto the closed wall so parcel motion nearly disappears while the pressure cue stays strong.
Resonance in Air Columns / Open and Closed Pipes
Compare open and closed pipe boundary conditions on one compact air column so standing-wave shapes, missing even harmonics, probe motion, and pressure cues stay tied to the same resonance state.
Not started on this browser yet.
Enter compare mode, keep both setups at the same tube length and the same resonance-order slider setting of 2, then make Setup B the closed-open tube so Setup A lands on the 2nd harmonic while Setup B lands on the 3rd harmonic at a lower frequency.
Resonance in Air Columns / Open and Closed Pipes
Compare open and closed pipe boundary conditions on one compact air column so standing-wave shapes, missing even harmonics, probe motion, and pressure cues stay tied to the same resonance state.
Not started on this browser yet.
Starting from the reference orbit, keep the radius close to the original circle but shorten the period to about $2.2\,\mathrm{s}$. Land the motion in the speed and centripetal-acceleration bands that go with that stronger centripetal-force requirement.
Uniform Circular Motion
Track a particle moving at constant speed around a circle and connect radius, angular speed, tangential speed, centripetal acceleration, and the inward-force requirement to the same live state.
Not started on this browser yet.
Open compare mode and keep Setup A and Setup B on nearly the same period, but make Setup B need the larger centripetal pull by giving it the wider orbit.
Uniform Circular Motion
Track a particle moving at constant speed around a circle and connect radius, angular speed, tangential speed, centripetal acceleration, and the inward-force requirement to the same live state.
Not started on this browser yet.
Starting from the reference orbit, tune the motion until the inward acceleration sits in the $7$ to $8.5\,\mathrm{m/s^2}$ band while the tangential speed stays between $2.5$ and $3.1\,\mathrm{m/s}$.
Uniform Circular Motion
Track a particle moving at constant speed around a circle and connect radius, angular speed, tangential speed, centripetal acceleration, and the inward-force requirement to the same live state.
Not started on this browser yet.
Open compare mode from the reference orbit and make Setup B complete turns noticeably faster than Setup A while both setups keep nearly the same radius.
Uniform Circular Motion
Track a particle moving at constant speed around a circle and connect radius, angular speed, tangential speed, centripetal acceleration, and the inward-force requirement to the same live state.
Not started on this browser yet.
Starting from Free swing, switch into the response view and tune the driver until it sits very close to resonance with a strong steady-state response.
Damping / Resonance
Explore how damping removes energy, how driving frequency changes amplitude, and why resonance becomes dramatic near the natural frequency.
Not started on this browser yet.
From Free swing, make the transient decay quickly enough that a late inspected sample shows only a very small displacement.
Damping / Resonance
Explore how damping removes energy, how driving frequency changes amplitude, and why resonance becomes dramatic near the natural frequency.
Not started on this browser yet.
Build a vector whose horizontal and vertical components are nearly the same size. Keep the component graph open so the match is visible in the real readout.
Vectors and Components
Rotate and scale a live vector, decompose it into horizontal and vertical parts, and watch those components drive the same straight-line motion and geometry.
Not started on this browser yet.
Pause at the end of the $4\,\mathrm{s}$ walk and make the point land near $(16\,\mathrm{m}, 12\,\mathrm{m})$.
Vectors and Components
Rotate and scale a live vector, decompose it into horizontal and vertical parts, and watch those components drive the same straight-line motion and geometry.
Not started on this browser yet.
Keep the push point near the handle but make the bar feel almost no turning effect.
Torque
Push on one pivoted bar and see how lever arm distance, force direction, and turning effect stay tied to the same compact rotational bench.
Not started on this browser yet.
Open compare mode and make Setup B twist just as hard as Setup A even though Setup B pushes much closer to the pivot.
Torque
Push on one pivoted bar and see how lever arm distance, force direction, and turning effect stay tied to the same compact rotational bench.
Not started on this browser yet.
Pause at the end of the clip and tune a clean clockwise twist.
Torque
Push on one pivoted bar and see how lever arm distance, force direction, and turning effect stay tied to the same compact rotational bench.
Not started on this browser yet.
Keep the motor near the baseline torque, then make the rotor spin up sharply by changing only the mass layout.
Rotational Inertia / Moment of Inertia
Keep the same total mass and torque, then slide equal masses inward or outward to see why moment of inertia makes some rotors much harder to spin up than others.
Not started on this browser yet.
Open compare mode and make Setup B much harder to spin than Setup A without changing the torque in either setup.
Rotational Inertia / Moment of Inertia
Keep the same total mass and torque, then slide equal masses inward or outward to see why moment of inertia makes some rotors much harder to spin up than others.
Not started on this browser yet.
Pause at the end of the clip and tune a wide-rim rotor that still reaches a moderate final angular speed.
Rotational Inertia / Moment of Inertia
Keep the same total mass and torque, then slide equal masses inward or outward to see why moment of inertia makes some rotors much harder to spin up than others.
Not started on this browser yet.
Starting from Tips right, move the support center until the heavy right load is back in static equilibrium.
Static Equilibrium / Centre of Mass
Shift one support region under one loaded plank and see how centre of mass, support reactions, and torque balance decide whether the object stays stable or tips.
Not started on this browser yet.
Starting from Support under load, shift the support region left until the plank is only just stable but not yet tipping.
Static Equilibrium / Centre of Mass
Shift one support region under one loaded plank and see how centre of mass, support reactions, and torque balance decide whether the object stays stable or tips.
Not started on this browser yet.
Open compare mode. Keep Setup A on Support under load, then tune Setup B so a heavier cargo placed closer in lands on the same combined centre of mass.
Static Equilibrium / Centre of Mass
Shift one support region under one loaded plank and see how centre of mass, support reactions, and torque balance decide whether the object stays stable or tips.
Not started on this browser yet.
Start from the lab baseline, then build a wide layout that still carries nearly the same angular momentum.
Angular Momentum
Treat angular momentum as rotational momentum on one compact rotor where mass radius and spin rate stay tied to the same readouts, response maps, and same-L conservation story.
Not started on this browser yet.
Open compare mode and make Setup A compact and Setup B wide while keeping their angular momenta nearly matched.
Angular Momentum
Treat angular momentum as rotational momentum on one compact rotor where mass radius and spin rate stay tied to the same readouts, response maps, and same-L conservation story.
Not started on this browser yet.
Pause at the end of the clip and tune a wide same-L rotor whose slow spin makes the accumulated angle stay small.
Angular Momentum
Treat angular momentum as rotational momentum on one compact rotor where mass radius and spin rate stay tied to the same readouts, response maps, and same-L conservation story.
Not started on this browser yet.
Keep the ramp near its baseline angle and tune the roller so it reaches the bottom in under about $1.85\,\mathrm{s}$.
Rolling Motion
Roll a sphere, cylinder, hoop, or custom mass distribution down one incline and see how rolling without slipping ties translation, rotation, and rotational inertia to the same honest run.
Not started on this browser yet.
Open compare mode and make Setup B finish much later than Setup A while keeping both setups on the same slope and radius.
Rolling Motion
Roll a sphere, cylinder, hoop, or custom mass distribution down one incline and see how rolling without slipping ties translation, rotation, and rotational inertia to the same honest run.
Not started on this browser yet.
Inspect the run near the end and tune a small sphere that keeps the same rolling logic but reaches a high angular speed.
Rolling Motion
Roll a sphere, cylinder, hoop, or custom mass distribution down one incline and see how rolling without slipping ties translation, rotation, and rotational inertia to the same honest run.
Not started on this browser yet.
Starting from Earth shot, stretch the landing point into the $35$ to $38\,\mathrm{m}$ range while keeping the apex below about $10\,\mathrm{m}$.
Projectile Motion
Launch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.
Not started on this browser yet.
From Earth shot, pause exactly at the top of the arc where the vertical velocity has dropped to zero but the projectile is still high above the ground.
Projectile Motion
Launch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.
Not started on this browser yet.
Start from Level venturi and adjust only the throat width until the throat pressure is about 27.1 kPa while the entry state stays near baseline.
Bernoulli's Principle
Follow one steady ideal-flow pipe and see how pressure, speed, and height trade within the same Bernoulli budget while continuity keeps the flow-rate story honest.
Not started on this browser yet.
Start from Baseline venturi, switch to compare mode, leave Setup A alone, and tune Setup B until it keeps the same entry pressure and flow rate but recovers the throat pressure by widening only the throat.
Bernoulli's Principle
Follow one steady ideal-flow pipe and see how pressure, speed, and height trade within the same Bernoulli budget while continuity keeps the flow-rate story honest.
Not started on this browser yet.
Adjust the block so it could stay about half submerged without extra support.
Buoyancy and Archimedes' Principle
Use one immersed-block bench to connect pressure difference, displaced fluid, and the density balance behind floating, sinking, and neutral buoyancy.
Not started on this browser yet.
Start from Wood in water, switch to compare mode, leave Setup A alone, and tune only Setup B until the same block balances with a noticeably smaller submerged height in denser fluid.
Buoyancy and Archimedes' Principle
Use one immersed-block bench to connect pressure difference, displaced fluid, and the density balance behind floating, sinking, and neutral buoyancy.
Not started on this browser yet.
Starting from Reference orbit, make the source heavier while keeping the chosen radius near 1.6 m and the orbit circular.
Circular Orbits and Orbital Speed
See why a circular orbit needs the right sideways speed, how gravity supplies the centripetal acceleration, and how source mass and radius together set orbital speed and period on one bounded live model.
Not started on this browser yet.
Open compare mode and keep both setups circular with the same source mass, but make Setup B the smaller-radius orbit so it moves faster and finishes sooner.
Circular Orbits and Orbital Speed
See why a circular orbit needs the right sideways speed, how gravity supplies the centripetal acceleration, and how source mass and radius together set orbital speed and period on one bounded live model.
Not started on this browser yet.
Starting from Reference orbit, lower the speed just enough that gravity is clearly stronger than the turning requirement and the path bends inside the dashed circle.
Circular Orbits and Orbital Speed
See why a circular orbit needs the right sideways speed, how gravity supplies the centripetal acceleration, and how source mass and radius together set orbital speed and period on one bounded live model.
Not started on this browser yet.
Start from Uniform pipe and adjust only section B until the middle speed is about twice the section A speed while the same baseline flow rate is kept.
Continuity Equation
Keep one steady stream tube on screen and use Q = Av to connect cross-sectional area, flow speed, and the same volume flow rate through narrow and wide sections.
Not started on this browser yet.
Start from Baseline stream, switch to compare mode, leave Setup A alone, and tune Setup B until it keeps the same flow rate but slows section B down by widening that middle section.
Continuity Equation
Keep one steady stream tube on screen and use Q = Av to connect cross-sectional area, flow speed, and the same volume flow rate through narrow and wide sections.
Not started on this browser yet.
Starting from Baseline drop, tune the setup into a much slower terminal-speed case by keeping the mass near $2\,\mathrm{kg}$ while increasing both area and drag strength.
Drag and Terminal Velocity
Drop one body through a fluid and use mass, area, and drag strength to see drag grow with speed until force balance settles into terminal velocity.
Not started on this browser yet.
Starting from Draggy disk, pause when the object is effectively at terminal speed: drag nearly equals weight and the remaining net downward force is tiny.
Drag and Terminal Velocity
Drop one body through a fluid and use mass, area, and drag strength to see drag grow with speed until force balance settles into terminal velocity.
Not started on this browser yet.
Starting from Dipole reference, turn the source pair into an equal positive arch so the horizontal field cancels while the net field still points upward.
Electric Fields
See how source-charge sign, distance, and superposition set the electric field at one probe, then watch a test charge turn that field into a force without changing the field itself.
Not started on this browser yet.
Starting from Like-charge arch, reverse the force on the test charge while keeping the same upward field symmetry at the probe.
Electric Fields
See how source-charge sign, distance, and superposition set the electric field at one probe, then watch a test charge turn that field into a force without changing the field itself.
Not started on this browser yet.
Starting from Axis near, move the probe to the doubled-distance case on the same horizontal line so the field magnitude falls to about one quarter of the 1 m reference.
Gravitational Fields
See how one source mass creates an inward gravitational field, how source mass and distance set the field strength, and how a probe mass turns that field into force without changing the field itself.
Not started on this browser yet.
Starting from Baseline diagonal, change only the probe mass so the force magnitude doubles while the gravitational field stays the same.
Gravitational Fields
See how one source mass creates an inward gravitational field, how source mass and distance set the field strength, and how a probe mass turns that field into force without changing the field itself.
Not started on this browser yet.
Starting from Axis 1 m, move the probe to the doubled-distance case on the same horizontal line so phi is about half as deep and the field magnitude is about one quarter as large.
Gravitational Potential and Potential Energy
See one source mass create a negative potential well, compare how potential and potential energy change with distance, and connect the downhill slope of phi to the gravitational field on the same live model.
Not started on this browser yet.
Starting from Baseline diagonal, change only the probe mass so the potential energy doubles in magnitude while the potential and field stay fixed.
Gravitational Potential and Potential Energy
See one source mass create a negative potential well, compare how potential and potential energy change with distance, and connect the downhill slope of phi to the gravitational field on the same live model.
Not started on this browser yet.
Start from Metal on cool bench, switch to compare mode, and edit only Setup B until it keeps nearly the same temperature contrast as Setup A but loses energy at less than half the rate.
Heat Transfer
See heat as energy transfer driven by temperature difference while conduction, convection, and radiation compete on one compact bench with honest pathway rates.
Not started on this browser yet.
Tune the live setup until radiation is the largest pathway while the block is still clearly hotter than the room.
Heat Transfer
See heat as energy transfer driven by temperature difference while conduction, convection, and radiation compete on one compact bench with honest pathway rates.
Not started on this browser yet.
Start from Room baseline and lower only the volume until the pressure is about double while the temperature and particle count stay near the baseline values.
Ideal Gas Law and Kinetic Theory
Connect pressure, volume, temperature, and particle number on one bounded particle box, then read the same pressure changes back as changes in particle speed and wall-collision rate.
Not started on this browser yet.
Start from Hotter same box, switch to compare mode, and edit only Setup B until it reaches about the same pressure while staying cooler and using more particles instead of more temperature.
Ideal Gas Law and Kinetic Theory
Connect pressure, volume, temperature, and particle number on one bounded particle box, then read the same pressure changes back as changes in particle speed and wall-collision rate.
Not started on this browser yet.
Start from Water baseline and adjust only the probe depth until the total pressure is about 24 kPa while the piston load, area, density, and gravity stay near baseline.
Pressure and Hydrostatic Pressure
Use one piston-and-tank bench to connect force per area, pressure acting in all directions, and the way density, gravity, and depth build hydrostatic pressure.
Not started on this browser yet.
Start from Water baseline, switch to compare mode, leave Setup A alone, and tune only Setup B until it reaches the same total pressure with a smaller surface-pressure part and a denser fluid.
Pressure and Hydrostatic Pressure
Use one piston-and-tank bench to connect force per area, pressure acting in all directions, and the way density, gravity, and depth build hydrostatic pressure.
Not started on this browser yet.
Start from Low-c warm sample, switch to compare mode, and edit only Setup B until both setups use the same 4 minute pulse but Setup B warms much less because its specific heat is larger.
Specific Heat and Phase Change
See why the same energy pulse changes different materials by different temperature amounts, and why a phase-change shelf can absorb or release energy without changing temperature on one compact thermal bench.
Not started on this browser yet.
Starting from Warming toward the shelf, pause on a real shelf moment where temperature is near 0 degC but the phase fraction is still between fully solid and fully liquid.
Specific Heat and Phase Change
See why the same energy pulse changes different materials by different temperature amounts, and why a phase-change shelf can absorb or release energy without changing temperature on one compact thermal bench.
Not started on this browser yet.
Start from the small warm sample, switch to compare mode, and edit only Setup B until it keeps about the same temperature as Setup A but clearly stores much more internal energy.
Temperature and Internal Energy
Compare average particle motion with whole-sample energy, vary amount and heating, and see why a phase-change shelf breaks naive temperature-only reasoning on one compact thermal bench.
Not started on this browser yet.
Starting from Warming toward a shelf, pause the run on a real shelf moment where temperature is nearly flat even though the sample is still taking in energy.
Temperature and Internal Energy
Compare average particle motion with whole-sample energy, vary amount and heating, and see why a phase-change shelf breaks naive temperature-only reasoning on one compact thermal bench.
Not started on this browser yet.
Starting from Dipole reference, tune the setup until the midpoint has almost zero field but still sits on a clearly positive potential hill.
Electric Potential
Map how source-charge sign and distance shape electric potential, compare potential differences across one honest scan line, and connect the downhill slope of V to the electric field.
Not started on this browser yet.
Open compare mode, keep the same source mass in both setups, and make Setup B the much wider circular orbit so it has the longer year.
Kepler's Third Law and Orbital Periods
Compare circular orbits around one source mass and see why larger orbits take longer: the path is longer, the circular speed is lower, and the same live model makes the period law visible without hiding the gravity-speed link.
Not started on this browser yet.
Starting from Baseline year, raise the source mass while keeping the same radius circular so the period becomes clearly shorter.
Kepler's Third Law and Orbital Periods
Compare circular orbits around one source mass and see why larger orbits take longer: the path is longer, the circular speed is lower, and the same live model makes the period law visible without hiding the gravity-speed link.
Not started on this browser yet.
Starting from Baseline year, lower the speed enough that the path is no longer the circular orbit Kepler's law is describing.
Kepler's Third Law and Orbital Periods
Compare circular orbits around one source mass and see why larger orbits take longer: the path is longer, the circular speed is lower, and the same live model makes the period law visible without hiding the gravity-speed link.
Not started on this browser yet.
Starting from the matched series pair, change only the circuit structure needed to give each branch the full battery voltage and make the total current land near 4 A.
Basic Circuits
Keep one battery and two resistors in view while current, voltage, resistance, Ohm's law, and the contrast between series and parallel all stay tied to one honest circuit.
Not started on this browser yet.
Starting from High but bound, raise the launch just to the threshold case at the same source mass and launch radius so the total specific energy is about zero and the finite turnaround disappears.
Escape Velocity
Launch outward from one bounded gravity source and see how source mass, launch radius, and total specific energy decide whether the object escapes or eventually returns.
Not started on this browser yet.
Starting from Threshold launch, tune a launch that still begins from 1.6 m around a 4 kg source, climbs high, but remains bound with a finite turnaround near 10.4 m.
Escape Velocity
Launch outward from one bounded gravity source and see how source mass, launch radius, and total specific energy decide whether the object escapes or eventually returns.
Not started on this browser yet.
Starting from Aligned pass, tune the bench until the detector reads about one half of the incoming intensity for a linear input.
Polarization
Use one compact polarizer bench to see polarization as the orientation story of transverse waves, how angle mismatch sets transmitted light, and why one ideal polarizer makes unpolarized light emerge with one chosen axis.
Not started on this browser yet.
Starting from Crossed axes, switch the bench to an unpolarized first-pass case that still leaves the detector near half brightness.
Polarization
Use one compact polarizer bench to see polarization as the orientation story of transverse waves, how angle mismatch sets transmitted light, and why one ideal polarizer makes unpolarized light emerge with one chosen axis.
Not started on this browser yet.
Starting from Wide slit, tune the controls until the first minimum lands between 22 deg and 28 deg.
Diffraction
Watch a wave spread after one narrow opening, see why diffraction grows when wavelength competes with slit width, and build the wave-optics bridge toward double-slit interference.
Not started on this browser yet.
Starting from Center bright, move the probe onto the first dark band without changing the slit or wavelength.
Diffraction
Watch a wave spread after one narrow opening, see why diffraction grows when wavelength competes with slit width, and build the wave-optics bridge toward double-slit interference.
Not started on this browser yet.
Starting from Center bright, move the probe onto the first dark fringe without changing wavelength, slit separation, or screen distance.
Double-Slit Interference
Use two coherent slits and one screen to connect path difference, phase difference, and fringe spacing to wavelength, slit separation, and screen distance on one compact optics bench.
Not started on this browser yet.
Starting from Tight fringes, tune the geometry until the bright-fringe spacing lands between 1.8 m and 2.1 m.
Double-Slit Interference
Use two coherent slits and one screen to connect path difference, phase difference, and fringe spacing to wavelength, slit separation, and screen distance on one compact optics bench.
Not started on this browser yet.
Starting from Gentle glow, keep the 8 ohm load and raise the source until the stage power bar settles near 18 W.
Power and Energy in Circuits
Keep one source and one resistive load in view while current, power, and accumulated energy over time stay tied to the same honest circuit.
Not started on this browser yet.
Starting from Air to glass, tune the setup until the refracted angle lands between 25 and 28 degrees while the speed ratio v2/v1 stays between 0.62 and 0.69.
Refraction / Snell's Law
Watch one light ray cross a boundary, connect refractive index to speed change, and see Snell's law set the refracted angle, bending direction, and critical-angle limit on the same live diagram.
Not started on this browser yet.
Open compare mode from Air to glass. Leave Setup A near the baseline, then edit Setup B so the lower medium is noticeably denser and the incident angle is steeper.
Refraction / Snell's Law
Watch one light ray cross a boundary, connect refractive index to speed change, and see Snell's law set the refracted angle, bending direction, and critical-angle limit on the same live diagram.
Not started on this browser yet.
Starting from Crown green, tune the current wavelength and prism so the selected refractive index lands between 1.53 and 1.55 while the selected deviation lands between 11.0 and 12.0 degrees.
Dispersion / Refractive Index and Color
Use one compact thin-prism bench to see how refractive index can depend on wavelength, why different colors bend by different amounts, and how a bounded prism model separates colors without widening into a full spectroscopy subsystem.
Not started on this browser yet.
Open compare mode from Crown green. Keep Setup A weakly dispersive, then edit Setup B until the same prism angle produces a much larger red-violet spread.
Dispersion / Refractive Index and Color
Use one compact thin-prism bench to see how refractive index can depend on wavelength, why different colors bend by different amounts, and how a bounded prism model separates colors without widening into a full spectroscopy subsystem.
Not started on this browser yet.
Starting from Unequal series loads, rewire the setup so Load B keeps the full battery voltage while its branch current stays around 1 A.
Series and Parallel Circuits
Switch the same two loads between one loop and two branches, then track how current, voltage, brightness, and charge flow reorganize without changing the battery.
Not started on this browser yet.
Starting from Glass to air near critical, tune the setup until the incident angle stays just below theta_c: keep theta_1 - theta_c between -2 and -0.4 degrees while theta_2 remains between 74 and 89 degrees.
Total Internal Reflection
Push a ray from a higher-index medium toward a lower-index boundary, watch the critical angle emerge, and see the same live diagram hand off from ordinary refraction to full internal reflection.
Not started on this browser yet.
Starting from Glass to air below critical, raise the setup until the boundary is clearly above threshold while staying on the same media pair.
Total Internal Reflection
Push a ray from a higher-index medium toward a lower-index boundary, watch the critical angle emerge, and see the same live diagram hand off from ordinary refraction to full internal reflection.
Not started on this browser yet.
Starting from the balanced series group, switch the highlighted pair into the parallel case until the reduction card reads about 3 ohm for the grouped pair and about 7 ohm for the full circuit.
Equivalent Resistance
Reduce one highlighted resistor group into an equivalent block, then collapse the whole mixed circuit honestly and watch how the total current and grouped behavior change together.
Not started on this browser yet.
Starting from the concave real-image preset, tune the setup until the image distance lands between 1.0 and 1.2 m and the magnification lands between -1.4 and -1.1.
Mirrors
Use plane, concave, and convex mirrors to track equal-angle reflection, signed image distance, and magnification on the same live ray diagram.
Not started on this browser yet.
Starting from the inside-focus preset, make a virtual upright image with $d_i$ between -0.90 and -0.75 m and magnification between 2.2 and 2.6.
Mirrors
Use plane, concave, and convex mirrors to track equal-angle reflection, signed image distance, and magnification on the same live ray diagram.
Not started on this browser yet.
Starting from Approach and pass, hold the magnet near the coil center so the coil still links strong flux while the induced emf collapses nearly to zero.
Faraday's Law and Lenz's Law
Track one magnet passing one coil and see how changing magnetic flux linkage creates induced emf while Lenz's law fixes the response direction, with the stage, galvanometer, and graphs all driven by the same bounded motion.
Not started on this browser yet.
Pause during the left-side approach so the magnet is still outside the coil, the linked flux is increasing, and the induced current runs in the clockwise Lenz response.
Faraday's Law and Lenz's Law
Track one magnet passing one coil and see how changing magnetic flux linkage creates induced emf while Lenz's law fixes the response direction, with the stage, galvanometer, and graphs all driven by the same bounded motion.
Not started on this browser yet.
Starting from the converging reference, tune the setup until the image distance lands between 1.0 and 1.2 m and the magnification lands between -1.4 and -1.1.
Lens Imaging
Trace principal rays through converging and diverging lenses, connect the signed thin-lens equation to the diagram, and watch image distance and magnification respond to the same object setup.
Not started on this browser yet.
Starting from the diverging reference, make a virtual image with d_i between -0.65 and -0.45 m and magnification between 0.3 and 0.5.
Lens Imaging
Trace principal rays through converging and diverging lenses, connect the signed thin-lens equation to the diagram, and watch image distance and magnification respond to the same object setup.
Not started on this browser yet.
Starting from Same-current sweep, reverse Wire B so the sideways contributions nearly cancel while the net magnetic field points strongly upward above the midpoint.
Magnetic Fields
See how current direction, wire spacing, distance, and superposition set the magnetic field around one or two long straight wires, with the stage arrows and scan graphs tied to the same live source pattern.
Not started on this browser yet.
Open compare mode from Opposite-current lift. Keep Setup A on the upward above-midpoint bridge, but turn Setup B into the midpoint-cancel case where the net field nearly vanishes even though the current magnitudes still match.
Magnetic Fields
See how current direction, wire spacing, distance, and superposition set the magnetic field around one or two long straight wires, with the stage arrows and scan graphs tied to the same live source pattern.
Not started on this browser yet.
Starting from Positive bends down, change the setup so the moving charge force points downward while the wire-segment force points upward for the same rightward direction.
Magnetic Force on Moving Charges and Currents
Launch one moving charge through a uniform magnetic field, compare it with a same-direction current segment, and connect force direction, curvature, and current-based force on one bounded live stage.
Not started on this browser yet.
Open compare mode from Positive bends down. Keep Setup A as the baseline, but make Setup B show the bigger moving-charge force and the wider orbit that go with a faster charge in the same field.
Magnetic Force on Moving Charges and Currents
Launch one moving charge through a uniform magnetic field, compare it with a same-direction current segment, and connect force direction, curvature, and current-based force on one bounded live stage.
Not started on this browser yet.
Starting from Blurred pair, tune the aperture or wavelength until the point spacing sits right on the Rayleigh limit.
Optical Resolution / Imaging Limits
Image two nearby point sources through one finite aperture and see why diffraction, wavelength, and aperture diameter limit how sharply an optical system can separate them.
Not started on this browser yet.
Starting from Near threshold, make the split clearly visible without changing the detector sample control.
Optical Resolution / Imaging Limits
Image two nearby point sources through one finite aperture and see why diffraction, wavelength, and aperture diameter limit how sharply an optical system can separate them.
Not started on this browser yet.
Starting from Violet above threshold, make the collected current almost vanish without changing the frequency or work function.
Photoelectric Effect
Use one compact lamp-to-metal bench to see why light frequency sets electron emission, why intensity alone fails below threshold, and how stopping potential reads the electron energy honestly.
Not started on this browser yet.
Starting from Bright but still below threshold, keep the beam bright while proving the collector current can stay essentially zero.
Photoelectric Effect
Use one compact lamp-to-metal bench to see why light frequency sets electron emission, why intensity alone fails below threshold, and how stopping potential reads the electron energy honestly.
Not started on this browser yet.
Starting from Hydrogen-like emission, tune the gaps so only two visible lines remain while the spectrum still stretches from blue-visible to red-visible wavelengths.
Atomic Spectra
Link discrete emission and absorption lines to allowed energy-level gaps with one compact ladder-and-spectrum bench that keeps transitions, wavelengths, and mode changes tied together.
Not started on this browser yet.
Starting from Wide upper gap, switch into absorption and tune the ladder until you have three visible notches with a clear red-to-blue spread.
Atomic Spectra
Link discrete emission and absorption lines to allowed energy-level gaps with one compact ladder-and-spectrum bench that keeps transitions, wavelengths, and mode changes tied together.
Not started on this browser yet.
Starting from Slow electron, tune the speed until the fixed loop is close to one wavelength long without changing the particle mass.
de Broglie Matter Waves
Use one compact matter-wave bench to see how particle momentum sets wavelength, why heavier or faster particles get shorter wavelengths, and how whole-number loop fits form a bounded bridge toward early quantum behavior.
Not started on this browser yet.
Starting from Near one-fit electron, keep the speed near the same value but make the particle heavy enough that roughly two wavelengths fit around the loop.
de Broglie Matter Waves
Use one compact matter-wave bench to see how particle momentum sets wavelength, why heavier or faster particles get shorter wavelengths, and how whole-number loop fits form a bounded bridge toward early quantum behavior.
Not started on this browser yet.
Starting from Balmer beta, tune the live state until the active transition is the classic red Balmer line while the page stays in emission.
Bohr Model
Use a compact hydrogen bench to connect quantized energy levels, allowed transitions, and named spectral-line series while staying clear that Bohr is a useful historical model rather than the final quantum description.
Not started on this browser yet.
Starting from Lyman alpha emission, switch to the matching reverse excitation from the ground level while keeping the same ultraviolet wavelength.
Bohr Model
Use a compact hydrogen bench to connect quantized energy levels, allowed transitions, and named spectral-line series while staying clear that Bohr is a useful historical model rather than the final quantum description.
Not started on this browser yet.
Starting from Class-lab sample, scrub to about one half-life so the expectation is halved while the live tray stays slightly below it.
Radioactivity and Half-Life
Use one compact decay bench to see why each nucleus decays unpredictably, why large samples still follow a regular half-life curve, and how to read remaining-count graphs honestly.
Not started on this browser yet.
Starting from Small noisy sample, scrub to about one half-life so the live tray sits well below the smooth expectation and the spread is obvious.
Radioactivity and Half-Life
Use one compact decay bench to see why each nucleus decays unpredictably, why large samples still follow a regular half-life curve, and how to read remaining-count graphs honestly.
Not started on this browser yet.
Build a reflected graph whose transformed vertex lands near $(-1, 2.4)$. Keep the reference curve and shift guide on so the move stays tied to the base landmark.
Graph Transformations
Move one parent curve with honest controls so shifts, vertical scale, and reflections stay tied to the same overlaid graph and landmark points.
Not started on this browser yet.
Build a decay case where the target is about one quarter of the start, so the curve reaches it in about two half-lives.
Exponential Change / Growth, Decay, and Logarithms
Change one starting value, one rate, and one target so growth, decay, doubling or half-life, and logarithmic target time all stay tied to the same live curve.
Not started on this browser yet.
Build a reciprocal family where the true vertical asymptote sits near $x=-1$, the removable hole sits on positive $x$, and the right branch stays below the horizontal asymptote.
Rational Functions / Asymptotes and Behavior
Vary one shifted reciprocal family so domain breaks, vertical and horizontal asymptotes, intercepts, and removable-hole behavior stay tied to the same graph.
Not started on this browser yet.
Move to the right-hand turning point so the tangent is almost flat, then shrink delta x until the secant slope is almost flat there too.
Derivative as Slope / Local Rate of Change
Slide a point along one curve, tighten a secant into a tangent, and connect local steepness to the derivative graph without leaving the same live bench.
Not started on this browser yet.
Switch to the case where both one-sided values nearly agree, but the graph still is not continuous at $x=0$.
Limits and Continuity / Approaching a Value
Approach one target point from the left and right, compare the limiting height with the actual function value, and contrast continuous, removable, jump, and blow-up behavior on one honest graph.
Not started on this browser yet.
Move the width until the fixed-perimeter rectangle reaches the maximum area and the local area slope is essentially zero.
Optimization / Maxima, Minima, and Constraints
Move one rectangle width under a fixed perimeter, watch the area curve peak, and use the local slope to see why the square is the best constrained shape.
Not started on this browser yet.
Move the bound into a region where the source height is already negative, but the running total is still positive overall.
Integral as Accumulation / Area
Move one upper bound across a source curve and watch signed area build into a running total so accumulation stays visual instead of symbolic.
Not started on this browser yet.
Adjust the vectors until the resultant lands very close to the origin, but keep the scaled first vector clearly nontrivial so the cancellation has to be earned.
Vectors in 2D
Combine, subtract, and scale vectors on one plane so magnitude, direction, and components stay tied to the same live object.
Not started on this browser yet.
Start from the identity matrix and build a right shear that keeps the first basis vector near its original x-axis direction while the unit square becomes a right-leaning parallelogram. Keep the basis and square visible so the column story stays on the plane.
Matrix Transformations / Stretch, Shear, Reflection
Let one 2 by 2 matrix act on a grid, the basis vectors, and a sample shape so stretch, shear, reflection, and combined plane changes stay visual instead of symbolic-only.
Not started on this browser yet.
Build a multiplication case where z · w lands almost on the positive imaginary axis while the multiplier magnitude stays close to one.
Complex Numbers on the Plane
Read complex numbers as points and vectors on one plane, then keep addition and multiplication geometric instead of symbolic-only.
Not started on this browser yet.
Adjust $\vec{B}$ until the amber projection nearly collapses while both arrows stay clearly nonzero. Keep the angle marker and projection guide visible so the right-angle story stays geometric.
Dot Product / Angle and Projection
Keep two vectors, their angle, the signed projection of one onto the other, and the dot product visible together so alignment reads geometrically instead of as memorized cases.
Not started on this browser yet.
Build a curve that is clearly taller than it is wide, then pause when the point is near the y-axis and still moving quickly.
Parametric Curves / Motion from Equations
Keep x(t), y(t), the traced path, and the moving point visible together so shape and traversal stay distinct.
Not started on this browser yet.
Build a point in Quadrant II where the leftward x projection is noticeably larger in magnitude than the upward y projection. Keep the coordinate guides on so $r$, $\theta$, $x$, and $y$ stay tied to the same point.
Polar Coordinates / Radius and Angle
Keep one point visible in polar and Cartesian views at the same time so radius and angle turn directly into x and y on the plane.
Not started on this browser yet.
Start from the axis-crossing view, then push the point just into Quadrant II so cosine has flipped negative while sine is still strongly positive. Keep the projection guides and sign map on so the crossing stays visible.
Unit Circle / Sine and Cosine from Rotation
Keep one rotating point, its x and y projections, and the sine-cosine traces linked so the unit circle becomes the live source of both functions.
Not started on this browser yet.
Build a setup where the reaction is clearly active even though concentration stays modest. Keep the threshold cue and collision pulses on so the rate story stays visible.
Reaction Rate / Collision Theory
Keep one chemistry box visible so temperature, concentration, activation threshold, and catalysts can be read as changes in successful collisions instead of chemistry slogans.
Not started on this browser yet.
Start in Quadrant I and set the point so cosine is near 0.6 while sine is near 0.8. Keep the squared-projection graph open so the identity line stays in view while you tune the angle.
Trig Identities from Unit-Circle Geometry
Keep one rotating point and its projections visible so the core trig identities stay tied to geometry instead of detached symbol rules.
Not started on this browser yet.
Build a point whose ratio y / x is negative but whose full angle is clearly in Quadrant II, not Quadrant IV. Keep the angle-recovery graph open so the principal-angle output and the actual angle disagree visibly.
Inverse Trig / Angle from Ratio
Keep one polar point and its coordinate signs visible so inverse trig becomes angle-from-ratio reasoning with quadrant checks instead of a calculator-only output.
Not started on this browser yet.
Build a product-favored equilibrium from a reactant-heavy start, then let the forward and reverse rates come back together while the product share stays clearly above one-half.
Dynamic Equilibrium / Le Chatelier's Principle
Watch a reversible chemistry bench keep changing microscopically while the mixture settles toward a new balance after each disturbance.
Not started on this browser yet.
Set the bench to a 3 A + 2 B recipe with supplies that still finish four full batches together.
Stoichiometric Ratios and Recipe Batches
Keep one reaction recipe visible so stoichiometric ratios read as complete batches, not detached worksheet proportions.
Not started on this browser yet.
Keep the 2 A + 3 B recipe, but set the supplies so B is limiting and 3 A packets remain after the full-yield run.
Limiting Reagent and Leftover Reactants
Use one recipe bench to see which reactant caps the output first and why the other reactant can remain in excess.
Not started on this browser yet.
Use the matched 2 A + 3 B run and set percent yield to 75% so the actual output lands at 3.75 batches.
Percent Yield and Reaction Extent
Compare actual output with the same theoretical recipe cap so percent yield stays visual and honest on one shared bench.
Not started on this browser yet.
Starting from a fairly crowded beaker, lower the concentration clearly while keeping the solute amount near the same starting value.
Concentration and Dilution
Use one beaker to separate how concentration changes when you add solvent from how it changes when you add more solute.
Not started on this browser yet.
Starting from a saturated beaker, make the excess pile disappear while keeping the same total solute amount.
Solubility and Saturation
Keep dissolved amount, excess solid, and current capacity in one beaker so saturation reads like a visible limit instead of a slogan.
Not started on this browser yet.
Adjust the mixture until the pH sits near neutral while acid and base character stay visibly close together.
Acid-Base / pH Intuition
Keep acid amount, base amount, water, and the pH strip visible together so acidity and basicity stay intuitive rather than memorized.
Not started on this browser yet.
Build a case where insertion sort finishes a nearly sorted list with very few writes.
Sorting and Algorithmic Trade-offs
Watch sorting as visible work on a live list so input order, comparisons, and writes stay concrete instead of collapsing into one final answer.
Not started on this browser yet.
Starting from the unbuffered acid pulse, keep the pH near neutral by adding buffer reserve while keeping the same acid push and without flooding the beaker with extra water.
Buffers and Neutralization
Keep neutralization, buffer reserve, and the pH strip visible together so steady pH does not look like unchanged chemistry.
Not started on this browser yet.
Build a large ordered list where the target sits near the far-right edge, but binary search still finds it in five checks or fewer.
Binary Search / Halving the Search Space
Keep an ordered list, the low-mid-high markers, and the shrinking interval visible together so binary search feels visual instead of procedural.
Not started on this browser yet.