Drag out from the launcher to aim — release to fire
The Sun drags its planets across the galaxy, so every orbit you see here is really a helix. Nine AQA modules are built the same way — every hard idea is a live model you can grab, change, and watch the equation fall out of.
Nine connected AQA modules ordered from measurement fundamentals to fields — every hard idea is a live model you can grab, scrub and interrogate, backed by required practicals, animated derivations and specification tracking.
two coherent sources a distance s apart
geometry → fringe spacing
Light through two narrow slits a distance s apart makes two in-step wave sources.
To reach a point on the screen, light from one slit travels an extra distance Δ = s sinθ.
A bright fringe forms when that extra path is one whole wavelength: s sinθ = λ.
D is large, so the angle is tiny: sinθ ≈ tanθ = w/D, where w is the fringe spacing.
Combine: s·(w/D) = λ, so w = λD/s. Longer λ or bigger D spreads the fringes; wider s squeezes them.
watch crests overlap — bright where they reinforce
w = λD / s
bright central maximum, dimmer side maxima
width = 2λD / a
each order is a sharp diffracted beam
d sinθ = nλ
nodes stay still, antinodes oscillate
1st harmonic (fundamental)
refraction, or total internal reflection
refraction
electrons drift and collide with the lattice
collisions → resistance
Free electrons drift through the metal but keep bumping into the fixed lattice atoms. Those collisions turn electrical energy into heat — that is resistance.
Make the wire twice as long and each electron runs past twice as many atoms — twice the collisions. So R ∝ L.
Double the cross-section and you open twice as many lanes; the current spreads out and resistance halves. So R ∝ 1/A.
Copper lets electrons slip through; nichrome fights them. That built-in “how hard is it” factor is the resistivity ρ.
Combine all three: R = ρL/A. Long, thin, resistive → high R; short, fat, conductive → low R.
the cell transfers energy to charge; the component transfers it onward
similar words, different physical meanings
Rate of charge flow: I = Q/t. Current is not “used up”.
Energy transferred per coulomb: V = W/Q.
Ratio of potential difference to current: R = V/I.
Energy transferred each second: P = W/t = VI.
I = ε / (R + r) · terminal V = ε − I·r
V = ε − I·r
resistance of a uniform conductor
Copper
V
Idle — press Charge
Ohmic resistor
on the curve
how R, I and V distribute
same current everywhere
Vout = Vin · R2 / (R1 + R2)
fixed resistors
Metal conductor
resistance rises with T
light arrives as photons of energy hf
energy in → energy out
Light delivers energy in photons, each carrying E = hf.
A single photon gives ALL its energy to one electron — all-or-nothing, not gradual.
To leave the metal the electron must first spend at least the work function φ.
Energy is conserved: hf = φ + KEmax, so KEmax = hf − φ.
If hf < φ no electron escapes — brighter light won't help. The threshold is f0 = φ/h.
photons in, electrons out — if the frequency is high enough
gradient = h · intercept = −φ
the experiment that proved light comes in quanta
hydrogen: Eₙ = −13.6 / n² eV
transition
why atoms only emit certain colours
the wave nature of a moving electron
λ = h / p
de Broglie's idea, confirmed by experiment
energy can become mass
energy → mass
Einstein's E = mc² runs both ways: enough concentrated energy can turn into mass.
You can't create a lone electron — that breaks charge and lepton-number conservation. You always get a particle AND its antiparticle: e⁻ + e⁺.
Creating each particle costs its rest energy mc². For the pair, that's 2mc².
A photon of energy hf provides the energy, so it needs at least 2mc²: hf ≥ 2mc².
At threshold hf = 2mc² (any extra becomes kinetic energy). Run it backwards and you get annihilation: e⁻ + e⁺ → 2γ.
tap one to inspect it
–
every particle is either a hadron, a lepton, or a force carrier
building a baryon (3 quarks)
computed from its quarks
click these quark combinations in the slots above
a neutron turns into a proton
the weak interaction, step by step
Feynman diagram — the W carries the change
| Quantity | before | after |
|---|
displacement from equilibrium
restoring force → simple harmonic motion
Pull the mass a distance x from its rest position and let go.
The force is proportional to x and always points back to equilibrium: F = −kx.
F = ma, so ma = −kx.
Divide by m: a = −(k/m)x. That proportionality is the signature of SHM.
Writing ω² = k/m gives a = −ω²x, and T = 2π√(m/k).
displacement traces a sine; energy swaps KE ⇄ PE
mass on a spring
what makes motion "simple harmonic"
the same motion, three views, all in step
how the three curves line up
read it straight off the graphs
light damping
how quickly energy is lost
amplitude vs driving frequency
below resonance
horizontal and vertical motion, running independently
The dotted guides are the two motions on their own: constant speed across, free fall down. The curve is only their sum.
every value follows from u, θ and h
momentum is conserved; kinetic energy need not be
Restitution e sets how much relative speed survives: e = 1 keeps the kinetic energy, e = 0 sticks the trolleys together.
total momentum cannot change
tip-to-tail, then resolve into components
Drag either arrowhead on the diagram to set that force directly.
one force equivalent to both
elastic while the graph stays straight
Past the elastic limit the line bends and the sample keeps a permanent extension when unloaded.
the area under the line is the work done
the speed is constant; the velocity is not
The velocity arrow keeps its length and only turns. A turning vector still changes, and a changing velocity is an acceleration.
Newton II, applied to a turning object
subtract two velocity arrows and see where the change points
Shrink Δθ toward zero and Δv swings until it points straight at the centre. That limit is the centripetal direction.
chord length becomes arc length
change one quantity and watch the force respond
The graph is F against r for your chosen m and ω. The marker is where you are sitting on it.
F = mω²r
a telescope magnifies the ANGLE, not the size
angles → magnification
A star is a point too far to enlarge — a telescope makes the ANGLE its light subtends at your eye bigger. Magnification M = θe / θ0.
Parallel light from the object (angle θ0) is focused by the objective (focal length f0) to a small image of height h in its focal plane, so θ0 ≈ h / f0.
In normal adjustment the eyepiece is set so the image sits at ITS focal point too — focal length fe, much shorter.
The eyepiece turns that image back into parallel rays entering your eye at a bigger angle θe ≈ h / fe.
M = θe/θ0 = (h/fe)/(h/f0) = f0/fe. Long objective, short eyepiece → high magnification.
parallel in at angle α, parallel out at bigger angle β
magnification & resolution
why big telescopes use mirrors
the star's colour and its curve
from surface temperature
luminosity vs temperature (hot on the left)
where your star sits
the same lines, shifted toward red
Doppler + Hubble's law
signal generator → vibration generator → stretched string → hanging mass
fundamental mode: one half-wavelength fits the string
Wave speed on a string is v = √(T/μ). In the fundamental, L contains half a wavelength, so λ = 2L. Substituting into f = v/λ gives the equation.
Use a fiducial marker for node position; include the mass hanger in tension; avoid pulley friction and parallax.
electromagnet release and light-gate timing
the graph linearises accelerated motion
For release from rest, s = ut + ½at² becomes s = ½gt² because u = 0 and a = g. Therefore s is directly proportional to t² and gradient m = g/2.
Use a soft landing pad, measure height consistently, repeat and average, and use a large range of heights.
reference wire removes support movement and thermal expansion
a material property independent of specimen size
E = stress/strain. Stress = F/A and strain = ΔL/L. Dividing gives (F/A)/(ΔL/L) = FL/(AΔL).
Wear eye protection, secure the wire, add loads gently, use a long thin wire for measurable extension, and stay below the elastic limit.
ammeter in series, voltmeter across the test length
geometry separates the material from the sample
A longer wire has proportionally more resistance, while a larger cross-sectional area provides more parallel paths. Therefore R = ρL/A, rearranging to ρ = RA/L.
Use low current, open the switch between readings, avoid touching a hot wire, and measure diameter repeatedly because A ∝ d².
main scale + coincident vernier line; drag the amber grip
smallest division = 0.1 mm
uncertainty fixes the sensible precision
which uncertainty do you combine?
drag a point, or focus the graph and use arrow keys
uncertainty uses the endpoint estimate furthest from best fit
drag either source charge or the white test probe
vectors add; potential adds as a scalar
The same influence spreads over a spherical area 4πr².
Moving along one requires no work because ΔV = 0.
drag the satellite radially; the required orbital velocity updates
field, potential and circular orbit describe the same location
Zero is defined at infinity; energy must be supplied to escape the field.
Both gravitational force and inertia contain the satellite mass m.
the magnetic force turns velocity without changing speed
force is always perpendicular to velocity
Reverse Q and the curvature reverses; the radius stays the same.
For conventional positive charge, force is perpendicular to both B and v.
Do not just read the relationship. Change the variables, predict their effect, and engineer the exact result. Each mission accepts a small experimental tolerance.
Tick an item when you can explain it without looking. Every simulator link takes you to the relevant interactive module.
Bright paths show the quantities shared with your selected relationship.
Follow energy as it is transferred.