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Physics
66 conceptsSee one repeating system from displacement to acceleration and back again, with the math tied directly to the motion on screen.
Watch kinetic and potential energy trade places in simple harmonic motion while the total stays fixed by amplitude and spring stiffness.
Follow one traveling wave across the same medium and connect crest spacing, travel delay, source timing, and the relation v = f lambda on one honest live stage.
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.
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.
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.
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.
Superpose two coherent sources, trace their path difference to phase difference, and watch bright and dark regions emerge on the same live screen.
Track fixed nodes, moving antinodes, and harmonic mode shapes on one live string while the same probe trace shows the underlying oscillation in time.
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.
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.
Explore how damping removes energy, how driving frequency changes amplitude, and why resonance becomes dramatic near the natural frequency.
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.
Push on one pivoted bar and see how lever arm distance, force direction, and turning effect stay tied to the same compact rotational bench.
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.
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.
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.
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.
Push one cart with a timed force pulse and watch momentum, impulse, and force-time area stay tied to the same motion, readouts, and graphs.
Use two carts to see the conservation rule in action: with no outside push, the system's total momentum stays fixed even while each cart's momentum and speed change.
Collide two carts on one honest track, keep total momentum in view, and see how elasticity, mass, and incoming speed shape the rebound or stick-together outcome.
Launch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.
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.
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.
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.
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.
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.
Use one immersed-block bench to connect pressure difference, displaced fluid, and the density balance behind floating, sinking, and neutral buoyancy.
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.
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.
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.
See heat as energy transfer driven by temperature difference while conduction, convection, and radiation compete on one compact bench with honest pathway rates.
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.
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.
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.
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.
Map how source-charge sign and distance shape electric potential, read voltage as a difference across one shared horizontal scan line, and connect the downhill slope of V to the electric field.
Keep one parallel-plate capacitor on screen so geometry, stored charge, field strength, and stored electric energy stay tied to the same bounded battery-and-plates model.
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.
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.
Connect electromagnetic waves to visible light, color, frequency, and the broader spectrum while one compact stage keeps the spectrum rail, field-pair sketch, and medium-linked wavelength changes tied together.
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.
Keep one source and one resistive load in view while current, power, and accumulated energy over time stay tied to the same honest circuit.
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.
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.
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.
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.
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.
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.
Use one small circuit to see the two Kirchhoff habits: currents balance at a split, and voltage rises and drops balance around every closed path.
Use plane, concave, and convex mirrors to track equal-angle reflection, signed image distance, and magnification on the same live ray diagram.
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.
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.
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.
See what each Maxwell equation says physically, how sources and circulation differ, and why changing electric and magnetic fields together unify electricity, magnetism, and light.
See how changing electric and magnetic fields travel together as one rightward wave, with the local field pair, source-to-probe delay, and propagation cue all tied to the same compact live stage.
See why a magnetic field bends a moving charge sideways, why faster charges can make wider arcs, and how the same cross-product direction rule pushes a current-carrying wire.
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.
Keep one resistor-capacitor loop on screen so capacitor voltage, current, stored energy, and the time constant all stay tied to the same charging or discharging setup.
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.
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.
Keep one non-ideal source and one load on screen so emf, internal drop, terminal voltage, current, and wasted power stay tied to the same one-loop circuit.
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.
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.
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.
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.
Math
16 conceptsMove one parent curve with honest controls so shifts, vertical scale, and reflections stay tied to the same overlaid graph and landmark points.
Vary one shifted reciprocal family so domain breaks, vertical and horizontal asymptotes, intercepts, and removable-hole behavior stay tied to the same graph.
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.
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.
Move one target-distance slider inward from both sides, compare the finite-limit guide with the actual point, and separate continuous, removable-hole, jump, and blow-up behavior on one graph-first bench.
Move one rectangle width under a fixed 24 meter perimeter and watch height, area, and local slope respond together so the square maximum emerges from the same bench.
Drag one upper bound across a source curve, watch signed area and the accumulation graph update together, and separate current source height from the running total.
Combine, subtract, and scale vectors on one plane so magnitude, direction, and components stay tied to the same live object.
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.
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.
Read complex numbers as points and vectors on one plane, then keep addition and multiplication geometric instead of symbolic-only.
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.
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.
Keep x(t), y(t), the traced path, and the moving point visible together so shape and traversal stay distinct.
Keep one rotating point and its projections visible so the core trig identities stay tied to geometry instead of detached symbol rules.
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.
Chemistry
9 conceptsKeep one chemistry box visible so temperature, concentration, activation threshold, and catalysts can be read as changes in successful collisions instead of chemistry slogans.
Watch a reversible chemistry bench keep changing microscopically while the mixture settles toward a new balance after each disturbance.
Keep one reaction recipe visible so stoichiometric ratios read as complete batches, not detached worksheet proportions.
Use one recipe bench to see which reactant caps the output first and why the other reactant can remain in excess.
Compare actual output with the same theoretical recipe cap so percent yield stays visual and honest on one shared bench.
Use one beaker to separate how concentration changes when you add solvent from how it changes when you add more solute.
Keep dissolved amount, excess solid, and current capacity in one beaker so saturation reads like a visible limit instead of a slogan.
Keep acid amount, base amount, water, and the pH strip visible together so acidity and basicity stay intuitive rather than memorized.
Keep neutralization, buffer reserve, and the pH strip visible together so steady pH does not look like unchanged chemistry.
Computer Science
6 conceptsWatch sorting as visible work on a live list so input order, comparisons, and writes stay concrete instead of collapsing into one final answer.
Keep an ordered list, the low-mid-high markers, and the shrinking interval visible together so binary search feels visual instead of procedural.
Keep one live graph, one local neighborhood, and one frontier cue visible together so graph structure feels readable before traversal rules get formal.
Keep the queue frontier, visited count, and graph layers visible together so breadth-first search reads as a layered process instead of a procedure list.
Keep the stack frontier, current depth, and branch order visible together so depth-first search feels like disciplined backtracking instead of random wandering.
Use one cyclic graph to see which nodes are waiting, which are finished, and why repeat edges are skipped instead of reopening loops.
Topic pages and paths
Show topic pages and paths
These topic pages and paths stay available without crowding the search controls.
Enter the current math slice through graph transformations, rational-function asymptotes, exponential change, vectors, complex-plane geometry, trig identities, inverse-angle reasoning, polar coordinates, and parametric motion without leaving the same live-bench product language used elsewhere on the site.
Fastest honest route
Functions and Change is still the clearest bounded start, while the collection and goal-path links keep the newer subject layer one click away.
Enter the current chemistry slice through reaction-rate ideas, a stoichiometry-and-yield recipe branch, and a broader solutions-and-pH branch without leaving the same simulation-first product architecture.
Fastest honest route
Rates and Equilibrium is still the clearest bounded start, while the collection and goal-path links keep the newer subject layer one click away.
Starter track
Rates and EquilibriumLesson set
Rates and Equilibrium Lesson SetEnter the current computer-science slice through one bounded algorithms-and-search branch where visible list work now widens into one shared graph-traversal bench without leaving the product's simulation-first architecture.
Fastest honest route
Algorithms and Search Foundations is still the clearest bounded start, while the collection and goal-path links keep the newer subject layer one click away.
Starter track
Algorithms and Search FoundationsPlaylist
Algorithms and Search Playlist