Scale of the Universe
Traverse 44 orders of magnitude — from quarks to the observable universe — on a logarithmic slider.
Orders of Magnitude
Compare any two physical objects side-by-side and see how dramatic a factor of 10 really is.
Domains of Physics
Interactive map of the 7 pillars of physics — mechanics, thermodynamics, EM, optics, relativity, quantum, nuclear.
Unit Conversion
Convert between SI and CGS units — see factor-of-10 conversions for length, mass, force, energy, pressure.
Significant Figures
Watch rounding in action — see how measurements round to the correct number of significant figures.
Rounding Error Accumulation
See how small rounding errors compound over repeated calculations.
Absolute & Relative Error
Compare measured value with actual to compute absolute, relative, and percentage errors.
Error Propagation (Add/Sub)
Visualize how absolute errors add when quantities are added or subtracted.
Error Propagation (Mul/Div)
See how relative errors add when quantities are multiplied or divided.
Dimensional Formula
Pick powers of M, L, T and see canonical physical quantities with matching dimensions.
Dimensional Equation Checker
Check whether a physical equation is dimensionally consistent across classical formulas.
Derivation by Dimensions
Walk through 4 classic derivations — pendulum period, Bohr radius, projectile range, gravitational force.
Vernier Caliper
Measure a length to 0.01 cm with a live vernier scale — MSR + VSD × LC.
Screw Gauge (Micrometer)
Measure thicknesses to 0.001 cm with a circular thimble with 50 divisions.
Least Count & Zero Error
Apply zero-error correction to raw instrument readings — both positive and negative zero error.
Position–Time Graph
See how x(t) = x₀ + v₀t + ½at² unfolds — slope = velocity, curvature = acceleration.
Velocity–Time Graph
Linear v(t) from constant acceleration — area under curve = displacement.
Acceleration–Time Graph
Three-phase step function — area under a-t gives Δv.
Uniform Motion
Constant velocity — distance markers, looping track, reversible direction.
Uniform Acceleration
Ball with initial velocity and constant acceleration — live v and a arrows.
Free Fall
Drop a ball from any height — gravity arrow, v arrow, fall time, impact velocity.
Relative Velocity (1D)
Switch reference frames — ground, A, B — and see velocities transform.
Meeting Point Problems
Two objects with different initial positions and velocities — find when and where they meet.
Graph Interpretation Lab
Identify motion type from x-t / v-t / a-t graphs — 6 canonical scenarios.
Variable Acceleration
Numerically integrate a(t) — see v(t) emerge as the integral under a(t).
Vector Addition
Triangle and parallelogram law — add two vectors and read |R| and angle θ live.
Vector Components
Resolve a vector into Vₓ = V cosθ and Vᵧ = V sinθ with live projection lines.
Dot Product (Scalar)
A·B = |A||B|cosθ — see the projection of B onto A as theta varies.
Cross Product (Vector)
|A×B| = |A||B|sinθ — parallelogram area and right-hand rule direction.
Projectile Motion
Explore the physics of objects launched at an angle — trace trajectories, analyze velocity components, and understand range and height in real time.
Projectile: Angle Variation
Change angle θ and speed u — watch the parabola update and read R, H, T live.
Range vs Angle Curve
R = u²sin(2θ)/g — see the full curve and confirm max range at 45°.
Projectile from Height
Launch from a cliff — asymmetric trajectory with quadratic flight time.
Boat in a River
Boat velocity + river current — see the resultant path and drift angle.
Rain–Man Problem
Walker in vertical rain — compute umbrella tilt angle.
Uniform Circular Motion
Ball on a circle at constant ω — live v (tangent) and a (toward center) arrows.
Relative Motion
Visualize how motion appears different from different frames of reference. Understand relative velocity with interactive scenarios.
Newton's First Law
Inertia — object at rest stays at rest; object in motion stays in motion. Toggle friction to see the difference.
Newton's Second Law
F = ma — apply a force, change the mass, see acceleration respond in real time.
Newton's Third Law
Action–reaction pairs — equal magnitude, opposite direction, act on different bodies.
Newton's Laws of Motion
Experience all three laws of Newton through interactive demonstrations — from inertia to action-reaction pairs.
Free-Body Diagram Builder
Build FBDs for flat, push, inclined, and hanging scenarios — see all forces labelled.
Static vs Kinetic Friction
See the difference between fₛ (adjustable up to μₛN) and fₖ (constant) in action.
Friction & Inclined Planes
Explore static and kinetic friction on flat and inclined surfaces. Adjust angles and coefficients to see real-time effects.
Inclined Plane (with Friction)
Block on incline — compute gsinθ, gcosθ, friction, net acceleration, angle of repose.
Atwood's Pulley
Two masses over a pulley — live acceleration and tension from a = (m₂−m₁)g/(m₁+m₂).
Connected Blocks
Two blocks pulled by a force, connected by a string — compute shared a and tension T.
Elevator: Apparent Weight
N = m(g+a) — feel heavier going up, lighter going down, weightless in free fall.
Banked Road
Turn on a banked curve — compute vIdeal, vMax, vMin with and without friction.
Force Resolution
Resolve a force at angle θ into Fx = F cosθ, Fy = F sinθ — see the components in real time.
Angle of Repose
Tilt the incline until the block just slides — see θ_repose = tan⁻¹(μ_s) emerge.
Wedge Problems (frictionless)
Block on movable wedge — both accelerate. See the recoil and coupled motion.
Centripetal Force (String)
Mass on a string in circular motion — tension provides T = mv²/r live.
Work by Constant Force
W = Fd cosθ — see the horizontal component pull the block while F is applied at angle θ.
Work–Energy Theorem
W_net = ΔKE — apply a force and watch kinetic energy change exactly by the work done.
Kinetic Energy
KE = ½mv² — see KE scale quadratically with velocity via a live curve and ball.
Gravitational PE (Near Earth)
U = mgh — drop a ball from height h and watch PE convert to KE.
Spring Potential Energy
U = ½kx² — stretch a spring and see the parabolic U–x curve with live reading.
Conservation of Energy
Roller-coaster track — E = PE + KE stays constant; bars show the exchange.
Power Delivered
P = F·v — see instantaneous and average power grow as velocity increases.
Work by Variable Force
W = ∫F dx — see area under F(x) for linear, quadratic, or sinusoidal forces.
Elastic Collision (1D)
Both KE and momentum conserved — live v₁', v₂' from standard formulas.
Inelastic Collision
Balls stick together — momentum conserved, KE lost to heat/deformation.
Coefficient of Restitution
Drop a ball — each bounce loses energy; heights scale as h₀·e^(2n).
Spring-Mass SHM
Visualize simple harmonic motion with a spring-mass system. Watch energy transform between kinetic and potential forms.
Positive vs Negative Work
Switch force angle: 0° → +W, 180° → −W (friction), 90° → 0. See the sign change.
Energy Loss to Friction
Block slides on rough floor — KE drops as heat: see d_stop = v₀²/(2μg).
Center of Mass
x_COM = Σmᵢxᵢ / Σmᵢ — drag 3 masses and watch the COM marker shift.
Motion of COM
v_COM is constant when F_ext = 0 — see COM move in a straight line despite collisions.
Linear Momentum
p = mv — momentum scales linearly with velocity; KE scales quadratically.
Impulse & Momentum
J = FΔt = Δp — before/after view with momentum change computed.
Momentum Conservation (Explosion)
Stationary body explodes into two — m₁v₁ + m₂v₂ = 0 demonstrated live.
Angular Momentum of a Particle
L = r × p = mr²ω — rotating ball with L vector (out of page).
Rocket Propulsion
F_thrust = u(dm/dt) — rocket loses mass and gains velocity.
Angular Kinematics
ω = ω₀ + αt, θ = ω₀t + ½αt² — see disk spin with live ω(t) and θ(t) plots.
Moment of Inertia
I formulas for 6 common shapes — solid/hollow sphere, cylinder, rod.
Torque
τ = r × F = rF sinθ — drag angle and watch rotation direction flip.
Parallel Axis Theorem
I = I_cm + Md² — shift the axis and see I grow quadratically with d.
Rotational Kinetic Energy
KE_rot = ½Iω² — compare with translational KE for rolling objects.
Conservation of Angular Momentum
L = Iω conserved — pull string shorter, ω grows as (r₀/r)².
Rolling Motion
a = g sinθ/(1 + k²) — 4 shapes race down an incline; sphere wins.
Linear ↔ Angular Variables
v = ωr, a_t = αr, a_c = ω²r — drag a particle on a rotating disc to see all three.
Lever Balance (Torque)
Two masses on a beam — adjust weights and arms; see torque balance live.
Radius of Gyration
k = √(I/M) — see equivalent ring radius for ring, disc, rod, sphere, shell.
Rolling With Slipping
Independent v and ω — detect skidding (v > ωR) vs spinning (ωR > v) vs pure rolling.
Gyroscopic Precession
Spinning top — see L precess about vertical at Ω = mgr/(Iω). Real animatronic feel.
Newton's Law of Gravitation
F = Gm₁m₂/r² — inverse-square force between two masses.
g at Height & Depth
g(r) ∝ r inside, 1/r² outside — single curve across both regions.
Gravitational Potential
V(r) = −GM/r — well shape with smooth transition at the surface.
Escape Velocity
v_esc = √(2GM/R) — launch a rocket with various v₀ and see if it escapes.
Orbital Velocity
v_orb = √(GM/r) — satellite at altitude h with period and g(h).
Kepler's Laws
Elliptical orbit with Sun at focus — equal-area sweep demonstrated live.
Orbital Motion & Satellites
Launch satellites into orbit, adjust velocities, and observe Kepler's laws in action with stunning visuals.
Gravitational Superposition
Three masses; drag a probe and see net F as the vector sum from each.
Gravitational Field Lines
g points always toward masses — single mass and binary system fields.
Geostationary Satellite
Tune altitude until T = 24h — satellite locks above the same point on Earth.
Stress–Strain Curve
Full σ–ε curve with proportional, elastic, yield, plastic, UTS and fracture zones. Watch a rod neck and snap.
Hooke's Law
σ = Yε — stretch a steel bar, watch ΔL grow linearly with F. Live σ–ε point on the Hooke line.
Young's Modulus Compared
Four wires (steel, copper, Al, brass) under same load — stiff materials stretch less.
Bulk Modulus
B = −ΔP/(ΔV/V) — cube compresses under hydrostatic pressure. 3D iso visual + live bar.
Shear Modulus
G = F/(Aφ) — block sheared into a parallelogram. Watch angle φ grow linearly with τ.
Poisson's Ratio
ν = −ε_T/ε_L — rod extends axially, contracts laterally. See the grid deform.
Elastic Potential Energy
U = ½σε·V — area under σ–ε curve fills as the wire stretches; energy bar grows live.
Pressure vs Depth
P = P₀ + ρgh — see pressure grow linearly with depth in any fluid.
Pascal's Law (Hydraulic Lift)
F₁/A₁ = F₂/A₂ — small input force lifts a heavy load via large piston.
Archimedes' Principle
F_b = ρ_fluid V_disp g — sink, float, suspend depending on density.
Floating vs Sinking
Compare 4 materials in one fluid — see who floats by density rule.
Streamline vs Turbulent (Re)
Re = ρvD/η — sweep velocity to cross from laminar to turbulent flow.
Equation of Continuity
A₁v₁ = A₂v₂ — pipe narrows; particles speed up. Live volume flow rate.
Bernoulli's Principle
P + ½ρv² + ρgh = const — manometers show pressure drop where speed is high.
Venturi Effect
Pipe with throat — flow accelerates, pressure plummets. Used in flow meters.
Airplane Lift
Curved airfoil — air on top is faster, pressure lower → net upward force.
Stokes' Law
F_drag = 6πηrv — viscous drag on a sphere through fluid.
Terminal Velocity
Sphere in viscous fluid — accelerates until weight = buoyancy + drag at v_t.
Capillary Rise
h = 2T cosθ/(ρgr) — narrow tube pulls liquid up by surface tension.
Surface Tension
Excess pressure inside drops/bubbles — ΔP = 2T/R (drop), 4T/R (bubble).
Linear Expansion
ΔL = L₀αΔT — see metals lengthen with temperature.
Area Expansion
β ≈ 2α — square sheet expanding in 2D.
Volume Expansion
γ — liquid level rises in a bulb.
Anomalous Water Expansion
Water density peaks at 4°C — unique behavior.
Heat ↔ Temperature
Q = mcΔT — same heat ≠ same ΔT (depends on c).
Calorimetry (Mixing)
T_eq = (m₁T₁ + m₂T₂)/(m₁+m₂) — mix two waters.
Conduction
dQ/dt = kA·ΔT/L — heat flow in a rod.
Thermal Conductivity Compared
Silver vs copper vs wood — see speed of heat flow.
Convection Currents
Natural convection — heated fluid rises, cools, sinks.
Radiation (Stefan–Boltzmann)
P = εσAT⁴ — blackbody vs polished surface.
Newton's Law of Cooling
Exponential decay to ambient temperature.
Phase Change & Latent Heat
Ice → water → steam: T plateaus during phase change.
Isothermal Process
PV = const — see hyperbola on PV plot.
Adiabatic Process
PV^γ = const — steeper than isotherm.
Isochoric Process
V = const, W = 0, Q = ΔU.
Isobaric Process
P = const, W = PΔV.
First Law of Thermodynamics
ΔU = Q − W — heat in, work out.
Work in Gas Expansion
W = ∫P dV — area under PV curve, 3 paths.
Heat Engine Cycle
Rectangular cycle on PV — η = W_net / Q_in.
Refrigerator / Heat Pump
COP = Q_c / W — work input pulls heat from cold.
Carnot Engine
η = 1 − T_c/T_h — ideal max efficiency.
Real vs Ideal Engine
Compare side-by-side — losses in real systems.
PV Diagram Explorer
Switch between 4 processes on a single plot.
T–S Diagram (Carnot)
Carnot rectangle — area = work done.
Cyclic Process
ΔU = 0, W = ∮P dV — engine vs refrigerator direction.
Internal Energy of Ideal Gas
U = (f/2) nRT — depends only on T.
Random Molecular Motion
Particles bounce inside a box, faster as T rises.
Wall Collisions → Pressure
Δp = 2mv per elastic hit — pressure builds.
Pressure from Molecular Theory
P = ⅓ ρ⟨v²⟩ — kinetic origin of pressure.
RMS / Avg / Most-Probable Speeds
Compare H₂, He, N₂, O₂, CO₂.
Temperature ↔ Kinetic Energy
⟨KE⟩ = (3/2) k_B T — linear in T.
Maxwell-Boltzmann Distribution
Speed distribution f(v) — peaks shift with T.
Boyle's Law
PV = const at fixed T.
Charles's Law
V/T = const at fixed P.
Pressure vs Temperature
P/T = const at fixed V (Gay-Lussac).
Mean Free Path
λ = 1/(√2 πd²n) — distance between collisions.
Degrees of Freedom
Mono / diatomic / polyatomic — Cv, Cp, γ.
Simple Harmonic Motion
x(t) = A cos(ωt + φ) — the canonical oscillation.
Displacement vs Time
Live x(t) graph with adjustable A, ω, φ.
Velocity vs Time
v = -Aω sin(ωt) — 90° lag from x.
Acceleration vs Time
a = -ω² x — 180° out of phase.
Spring-Mass Oscillator
ω = √(k/m), animated zigzag spring.
Vertical Spring (gravity)
x_eq = mg/k offset; period unchanged.
Energy in SHM (KE ↔ PE)
E = ½kA² constant — KE/PE swap.
Period vs Mass
T ∝ √m — square-root curve.
Period vs Spring Constant
T ∝ 1/√k — stiffer spring → faster.
Simple Pendulum
T = 2π√(L/g) — animated swing.
Pendulum: Length vs Period
T ∝ √L plot.
Pendulum: Effect of Gravity
Compare on Earth, Moon, Mars, Jupiter.
Damped Oscillations
Exponential decay envelope.
Forced Oscillations
Amplitude vs driving frequency curve.
Resonance (Mechanical)
Q-factor controls peak sharpness.
Transverse Wave
y(x,t) = A sin(kx − ωt) — particles oscillate ⟂.
Longitudinal Wave
Compressions / rarefactions along propagation.
Wave Propagation
Pulse moves at speed v across the medium.
Wavelength × Frequency (Mechanical)
v = fλ — see λ marker on the wave.
Wave Speed on a String
v = √(T/μ).
Interference
Constructive vs destructive at φ = 0° / 180°.
Beats
f_beat = |f₁ − f₂| — envelope visible.
Standing Wave on String
λ_n = 2L/n — nodes & antinodes.
Nodes & Antinodes
Highlighted N and A on a vibrating string.
Sound Wave Propagation
Concentric wavefronts from a point source.
Sound Speed in Media
Air vs water vs steel vs diamond.
Doppler — Source Moving
Pitch shifts as source approaches/recedes.
Doppler — Observer Moving
Observer's motion changes perceived frequency.
Doppler — Both Moving
f' = f(v±v_o)/(v∓v_s).
Harmonics on a String
f_n = nv/2L — first 6 harmonics.
Organ Pipe (Open / Closed)
Open: nv/2L. Closed: (2n−1)v/4L.
Energy Transport
P = ½μvω²A² — power along a string.
Phase Difference
φ = (2π/λ) Δx — visualize phase vs path.