Drag out from the launcher to aim — release to fire
EasyPhysics is a hands-on course. Every lesson is a simulation you drag, scrub and interrogate — and that needs a real screen and a real pointer.
open that on a laptop or desktop to start
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.
A lone photon cannot simply become a pair — energy and momentum could not both balance. A heavy nucleus sits close by and absorbs the recoil.
You can't create a lone electron — that breaks charge and lepton-number conservation. You always get a particle AND its antiparticle: e⁻ + e⁺.
In the detector's magnetic field the two tracks bend in opposite directions. That mirror-image pair is the signature of pair production.
Creating each particle costs its rest energy mc². For the pair, that's 2mc².
A photon of energy hf provides that energy, so it needs at least 2mc². At threshold hf = 2mc²; any extra becomes kinetic energy of the pair.
Every step reverses. An electron meeting a positron destroys both, and all of that mass — 2mc² — must reappear as energy.
A single photon could not conserve momentum: in the frame where the pair is at rest, total momentum is zero. Two photons leave back-to-back, each carrying mc².
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 |
|---|
solid — particles vibrating about fixed positions
kinetic + potential, added up over every particle
same particles, different amounts of energy
energy in against temperature rise
aluminium
the flat parts are where the bonds break
warming the ice
2.26 MJ/kg against 0.334 MJ/kg
holding temperature constant — Boyle's law
one mole, ideal
temperature is mean kinetic energy, nothing else
oxygen, 300 K
most pass straight through
where all the kinetic energy has become electric potential energy
1909, Geiger and Marsden
the strong nuclear force against electromagnetic repulsion
Below about 0.5 fm the strong force repels, which is what stops nucleons collapsing into one another. Between roughly 0.5 and 3 fm it attracts, pulling hardest near 1 fm, and past about 3 fm it has effectively vanished — it is very short range. Electromagnetic repulsion is weaker close in but falls off only as 1/r², so it is still pushing protons apart where the strong force can no longer reach. That is why heavy nuclei need extra neutrons to stay bound, and why no nucleus beyond bismuth is stable.
iron-56
r₀ = 1.2 fm
counting what is left
the chance per second
paper stops alpha
counts getting through
charge, mass and how far they travel
iron-56 sits at the top
the mass that goes missing
fission — splitting the heavy ones
U-235 + n
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 limit of proportionality the line starts to bend; past the elastic limit 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.
laser → slits or grating → screen
one bright fringe for each extra wavelength of path difference
A bright fringe appears where the paths from the two slits differ by a whole number of wavelengths. For small angles the path difference is sθ and the fringe sits at y = Dθ, so neighbouring fringes are λD/s apart. A grating does the same with hundreds of slits, giving sharp orders at d sin θ = nλ.
Never look into the laser or its reflections; use a low-power class 2 laser and a matt screen. Make D large and measure across many fringes to cut the percentage uncertainty.
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.
variable resistor, ammeter, voltmeter across the cell terminals
the cell's own resistance takes a share of every coulomb's energy
The emf ε is the energy the cell gives each coulomb. Some of it is used up inside the cell by its internal resistance r — the lost volts Ir — so the terminal pd is V = ε − Ir. That is y = c + mx with c = ε and m = −r.
Keep the current low and open the switch between readings: a warm cell has a different r. A protective resistor makes sure the cell is never shorted.
mass–spring and simple pendulum, timed from a fiducial marker
T² is proportional to m for a spring and to l for a pendulum
T = 2π√(m/k) is not a straight line against m, but squaring gives T² = (4π²/k)m, which is. The pendulum works the same way: T² = (4π²/g)l. The gradient then gives k or g directly.
Timing ten oscillations divides the reaction-time error by ten. Keep pendulum swings small (under about 10°) or T grows. Clamp the stand so it cannot topple, and keep feet clear of falling masses.
trapped air: pressure against volume, then volume against temperature
pV is constant at fixed T; V/T is constant at fixed p
Gas pressure comes from molecules hitting the walls. At fixed temperature, halving the volume doubles how often they hit, so p ∝ 1/V. At fixed pressure the volume grows in step with the absolute temperature, so extending l against θ to l = 0 lands at about −273 °C: absolute zero.
Wear eye protection with the pump and the acid bead, and never over-pressurise the tube. Hot water scalds: stir gently and let it cool before handling.
two-way switch, capacitor, resistor and voltmeter
an exponential decay becomes a straight line on a log scale
The pd falls by the same fraction in each equal time, so V = V₀e^(−t/RC). Taking natural logs gives ln V = ln V₀ − t/RC: a straight line with gradient −1/RC. After one time constant V has fallen to 37% of V₀.
Connect electrolytic capacitors the right way round and below their voltage rating. Discharge the capacitor fully before touching it.
top-pan balance, magnets on a steel yoke, a stiff wire through the gap
Newton's third law turns the force on the wire into a mass reading
The field pushes on the current with F = BIL, here upwards on the wire. By Newton’s third law the wire pushes down on the magnet with the same force, so the balance reads Δm = F/g more. F against I is a line through the origin with gradient BL.
Keep the wire at right angles to the field and measure L as the length between the poles. Currents of several amps warm the wire, so switch off between readings.
a search coil turned in an alternating field, read on an oscilloscope
only the part of B along the coil's normal links the coil
The flux through the coil is BA cos θ, with θ between the field and the coil’s normal. An alternating field keeps the flux linkage NBA cos θ sin ωt changing, inducing an emf with peak ε₀ = BANω cos θ. Facing the field (θ = 0) gives the most; edge-on (90°) gives none.
Keep the search coil at the centre, where the field is uniform, and keep the scope settings fixed while you turn the coil.
sealed source, GM tube on a rule, counter
gamma rays spread over a sphere of area 4πr²
Gamma rays spread out over a sphere, so the count rate falls as 1/r². The true distance is r = d + e, because the source sits a distance e inside its holder while d is measured from the outside. Then 1/√C = (d + e)/√k: a straight line that meets the d axis at −e.
Handle the source with tongs at arm’s length, pointing away from people. Keep the time near it short, return it to its lead box straight away, and wash your hands afterwards.
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.
AQA-STYLE QUESTIONS · REVEAL THE MARK SCHEME ONE MARK AT A TIME
Write the method before you reveal anything. Checking a scheme you have not attempted teaches recognition, not recall.
MARK SCHEME
two points on the curve, a distance h apart
a chord that dares to touch
Call the first point P. Put a second point Q a small distance further along — we’ll call that gap h.
Steepness is always “how far up” divided by “how far across”. Here that is the rise, divided by h.
Multiply out (x+h)², take away x², then divide by h. Everything simplifies to just 2x + h.
Make h smaller and smaller. The line pivots round P and settles onto one final position.
Once h has shrunk to nothing, 2x + h is simply 2x. That is the steepness of y = x² at any point x.
f(x) = x² above — its gradient, plotted live, below
differentiate any power of x on sight
the derivative is a new function, not one number
y = x³ − 3x — the ball hunts for f′ = 0
the second derivative decides
three steps, every exam
each curve is the gradient of the one above it
where a = −ω²x really comes from
calculus words, physics meaning
y = x² from 0 to 2 — 6 strips, midpoint sample
watch the strip sum close in on the exact area
integration before any rules
meet A(x) — the area collected so far
area, measured by its own growth
Sweep to the right and shade as you go. A(x) just means “how much area have I collected so far?”
Move a tiny bit further, h. The extra shaded bit is almost a rectangle: height f(x), width h. So the extra area is about f(x) × h.
Extra area ÷ h gives f(x). So the area is growing at exactly the height of the curve: dA/dx = f(x).
Here f = 2t, and the thing whose gradient is 2x is x². Sure enough, the area graph on the right is exactly x².
To get the area between a and b, you never add up strips — you read that same function at b, at a, and subtract.
v–t graph — the shaded area IS the displacement
rectangle + triangle = SUVAT
every one of these is ∫f dx
N = N₀e−λt — press Straighten to see the log view
curves hide constants; lines confess them
everything else is these, repeated
(1+x)⁴ — row 4 supplies the coefficients
term by term, watch it converge
(1+x)ⁿ ≈ 1 + nx when x is small
the cyan and mint heights stack into the gold curve
evaluate at each root — the other factor vanishes
simpler pieces unlock harder maths
each bounce reaches r × the last height
infinite bounces, finite distance
two families rule A-level
Pick an equation and watch it grow from a physical definition rather than a memorised line.
Follow energy as it is transferred.