Key ideas — A-level physics

Key ideas

The one or two sentences worth carrying out of every topic, one lesson at a time, straight from the notes. A fast last-minute skim, or a way to check a topic has actually stuck.

259 ideas

MeasurementsYear 123 topics

SI units and prefixes

Ten prefixes, and the booklet prints none of them.

Uncertainty and error

Averaging reduces random error, though it cannot remove it.
It does nothing to systematic error.
A power multiplies the percentage uncertainty by that power.

Estimation and orders of magnitude

Estimate before you calculate.
The calculator's answer must land near it.

MechanicsYear 1210 topics

Scalars and vectors

Vectors add tip to tail.
Only their components add as plain numbers.
Equilibrium closes the triangle.

Moments and equilibrium

Moments balance, not forces.
Use the perpendicular distance to the line of action.
Choose the pivot that eliminates the unknown.

Motion graphs and the SUVAT equations

Gradient and area read every graph.
SUVAT needs constant acceleration.

Projectile motion

Across, constant velocity.
Down, constant acceleration.
Time is the only thing the two columns share.

Newton's laws and the resultant force

Forces change motion, never sustain it.
Third-law pairs live on different bodies.

Mass and weight

Mass travels with you; weight belongs to where you are.

Drag and terminal speed

Drag grows with speed.
Terminal speed is where it catches the weight.

Momentum and impulse

No external force means momentum is conserved.
Kinetic energy is the one you have to check.
Elastic means approach speed equals separation speed.
Impulse is the area under a force-time graph.

Work, energy and power

Only the force along the motion does any work.

Conservation of energy

Energy is never used up.
It is moved, and you can always audit the move.

MaterialsYear 123 topics

Density and Hooke's law

The energy stored is the area under the force-extension graph.
½FΔL is that area only while the line is straight.

Stress, strain and the Young modulus

k describes the object.
E describes the material.
Reshape the sample and only one of them changes.

Fluids: pressure, upthrust and viscosity

Pressure is force per unit area, for a solid as much as a fluid.
Pressure in a fluid is depth times density times g.
Upthrust is the weight of fluid displaced.
Drag on a slow small sphere is Stokes' law, and nothing faster.

WavesYear 128 topics

Progressive waves

Energy travels. The particles only oscillate.

Longitudinal, transverse and polarisation

Transverse oscillates across the travel direction.
Longitudinal oscillates along it.
Only transverse waves can be polarised, and light can.

Stationary waves

Nothing travels along the string.
Adjacent nodes are half a wavelength apart.

Refraction and total internal reflection

Angles are measured from the normal.
TIR needs a lower n on the far side,
and an angle past the critical one.

Diffraction and the single slit

Every gap diffracts, and a gap near λ diffracts most.

Interference and Young's double slit

Bright where the paths differ by nλ.
Dark where they differ by (n + ½)λ.

Diffraction gratings

d sin θ = nλ.
sin θ can never pass 1, and that caps n.

Lenses and images

Power is one over the focal length, in metres.
Powers of lenses in contact add.
Real is positive, so a negative v is a virtual image.

Quantum phenomenaYear 124 topics

The photoelectric effect

Frequency sets whether electrons leave, and how fast.
Brightness sets only how many.

Collisions of electrons with atoms

Atoms accept exact gaps, or nothing.
The tube is that rule, run as a chain.

Energy levels and photon emission

Discrete lines mean discrete gaps.
Discrete gaps mean discrete levels.
One transition makes exactly one photon.

Wave-particle duality

Everything carries both behaviours, and momentum decides which one you see.

ParticlesYear 127 topics

Constituents of the atom

Z is the identity, A is the headcount, and specific charge audits both.

Stable and unstable nuclei

The strong force attracts out to 3 fm and repels inside 0.5 fm.
Every decay balances A and Z exactly.
The antineutrino exists because the beta spectrum is continuous.

Antimatter and photons

Same mass, opposite charge and opposite quantum numbers, every particle.
Rest energy sets the threshold in both directions.

Particle interactions and exchange particles

Forces are carried, not conjured, in all three Standard Model interactions.
Gravity has no tested exchange particle, and the graviton stays a proposal.
Only the weak interaction changes quark flavour.

Classification of particles

Hadrons feel the strong force. Leptons are fundamental.
Strangeness is born in pairs and broken only weakly.

Quarks and antiquarks

Baryons are three quarks. Mesons are a quark with an antiquark.
Antiquarks flip every sign.
The neutron's decay is one d becoming a u.

Conservation laws

Audit charge, baryon and lepton numbers, and strangeness.
Energy and momentum must be conserved as well.

ElectricityYear 126 topics

Current, charge and the direction problem

Conventional current runs plus to minus.
The electrons go the other way, slowly.
Both are true at once. Keep the labels on.

Current-voltage characteristics

R is the ratio V over I at a point, never the gradient of a curve.

Resistivity and superconductivity

R belongs to the wire.
ρ belongs to the material.

Circuits and Kirchhoff's laws

Charge is conserved at every junction.
Energy is conserved round every loop.
Series shares the current.
Parallel shares the pd.

Potential dividers

One current, so the shares follow the resistances.
Change a resistance and you move the share.

EMF and internal resistance

The emf is the energy per coulomb the cell supplies.
The terminal pd is what is left after the internal resistance.
The difference, Ir, grows with the current.

Periodic motionYear 134 topics

Circular motion

Circular motion is accelerated motion, aimed at the centre.
Something real has to supply the force.

Simple harmonic motion

Pushed back in proportion to how far you have gone, and the size of the swing never changes the time.

SHM systems: pendulums and springs

Springs count m and k. Pendulums count l and g.
The energy see-saws; the total holds still.
Damping drains the amplitude; light damping stretches the period only slightly.

Forced vibrations and resonance

Resonance occurs when the driving frequency equals the system's natural frequency.
Heavier damping lowers and broadens the response peak.

Thermal physicsYear 133 topics

Thermal energy transfer and specific heat capacity

Internal energy is random KE plus PE, summed over the particles.
Heating and working are the only two ways in.
A state change spends the energy on PE, so T stands still.

Ideal gases and the gas laws

Kelvin in every gas law, no exceptions.
Moles ride with R; molecules ride with k.

Molecular kinetic theory

Pressure is bombardment, derived from momentum.
Mean molecular kinetic energy is proportional to absolute temperature, and equals (3/2)kT.
c_rms is square, average, then root.
An ideal gas keeps no potential energy at all.

Gravitational fieldsYear 134 topics

The field concept

A field is a region that exerts force without touch.
Gravity and electrostatics share grammar; only charge can repel.

Newton's law of gravitation

Every mass pulls every other, as the inverse square.
Field strength is force per unit mass.
Measure r from the centre, every single time.

Gravitational potential

Potential is the work per kilogram to arrive from infinity, and it is always negative.
Gradient gives g from V; area gives ΔV from g.

Orbits and satellites

Kepler: an ellipse with the Sun at one focus, equal areas in equal times, and T² ∝ r³.
Gravity is the centripetal force; T² grows as r³.
Lower orbit, faster satellite, lower total energy.
Geostationary asks for a circle over the equator, 24 hours round it, and one fixed ring.

Electric fieldsYear 133 topics

Coulomb's law and electric field strength

Coulomb's law is the inverse square with charge in the seats.
Between plates E = V/d, and right-angle entry draws a parabola.

Electric potential

Potential is work per coulomb from infinity, and its sign follows the charge.
The size of the V against r gradient gives E, and the field points down the gradient; the area under E against r gives ΔV.
A volt is a joule per coulomb, never an amount of energy on its own.

Comparing electric and gravitational fields

One inverse-square shape, two casts of characters. Electricity wins by 10³⁶, and neutrality still hands the universe to gravity.

CapacitanceYear 133 topics

Capacitors and energy stored

Capacitance is charge parked per volt; the dielectric raises it.
Energy is the triangle under V against Q, and it grows as the voltage squared.

Charging and discharging

On discharge, Q, V and I fall along one shared curve.
On charging, Q and V climb while the current starts large and falls to zero.

The time constant and exponential decay

The time constant is RC: with R in ohms and C in farads, it comes out in seconds.
One time constant leaves 37%; every 0.69 of one halves the charge.
Log the data and the exponential plots as a straight line.

Magnetic fieldsYear 137 topics

Magnetic flux density and the force on a wire

The magnetic force acts on current, at right angles to everything.
One tesla puts one newton on every metre of crossing wire, per amp.

Force on a moving charge

F = BQv steers and never works, so the speed holds and the path curls.
Radius mv/BQ is momentum written as curvature.

Magnetic flux and flux linkage

Flux is field through area, linkage multiplies by the turns, and the cosine's angle always runs to the normal.

Electromagnetic induction: Faraday and Lenz

Emf is the rate of change of flux linkage.
Lenz turns the current against whatever caused it, to keep the energy books straight.
Spin a coil and out comes BANω times a sine.

Alternating currents

Alternating means reversing, and only a sinusoid puts rms at 0.707 of the peak.
Quoted ac is rms, the dc equivalent for power in the same resistor.
On the scope, squares become volts and seconds; f comes from 1/T.

Rectification and smoothing

Diodes make the current one-way; the bridge wastes neither half.
The reservoir capacitor rides over the gaps; ripple shrinks as RC grows.

Transformers

Turns set the voltage ratio; power only ever passes through.
The grid starves I²R with high volts, small current and tiny loss.

Nuclear physicsYear 136 topics

Rutherford scattering and the nuclear atom

Most alphas missed, so the atom is nearly all empty space.
The rare rebounds mark a nucleus that is tiny, massive and positive.
Subtract the background before any count rate does any work.

Radioactive decay and half-life

One nucleus is a coin toss; a mole of them is a clock.
Every half-life keeps the same fraction, so the count halves forever and never reaches zero.

Nuclear radius and density

R = R₀A^(1/3), so nuclear volume simply counts nucleons.
On the radius law, every nucleus, light or heavy, shares one density near 2 × 10¹⁷ kg m⁻³.
Closest approach only ever overestimates; electron diffraction measures.

Mass-energy and binding energy

A bound nucleus weighs less than its parts, and the gap is the binding energy.
Divide by A and iron-56 sits at the top of the curve, near 8.8 MeV per nucleon.

Fission and fusion

Both roads lead to iron, with heavy nuclei splitting and light nuclei fusing.
Sum the masses before and after; the missing u, times 931.5, is the MeV set free.

Nuclear reactors and safety

Moderator slows them, control rods absorb them to hold the chain at one, coolant carries the prize away.
Reactor fuel is far too dilute to detonate; overheating is the real danger.
Four layers of safety: shut it down, cool it, shield it, contain it.

ElectronicsYear 136 topics

Discrete semiconductor devices

No channel below the threshold voltage, so the drain current is negligible; in saturation above it the drain current climbs roughly with the square of the excess.
A MOSFET gate is insulated, so it takes no steady current and a logic pin can switch amps.
A zener holds its breakdown voltage across the load while the series resistor drops whatever is left.
Photocurrent follows the light; the Hall voltage follows the flux density.

Resonant circuits and filters

At resonance the two reactances cancel, and f0 depends on L and C alone.
Series resonance peaks the current, parallel resonance peaks the voltage, and both are a mass on a spring with L for the mass and C for the spring.
Q is the resonant frequency over the half-power bandwidth, so resistance lowers Q, broadens the peak and lets in more of what you did not want.

Operational amplifiers

With no feedback the op-amp only compares: a few hundred microvolts of difference send the output to a rail.
Negative feedback hands the gain to the resistors, and gain times bandwidth stays constant.
Inverting gain is minus Rf over Rin about a virtual earth; non-inverting gain is 1 + Rf over R1.

Summing and difference amplifiers

Each input rides its own gain, Rf over its own resistor, into a virtual earth; the output is minus the weighted sum.
The difference amplifier gives Rf over R1 times (V+ − V−), so interference shared by both inputs subtracts to nothing.
No output passes the supply rails; past them the amplifier saturates and clips.

Digital signal processing

A gate's output depends only on its present inputs; a flip-flop remembers one bit until the next clock edge.
EOR answers 1 when the inputs differ, and EOR with AND is the half-adder; NAND and NOR are AND and OR with the answer flipped.
Every toggling stage halves the frequency, so n stages divide by 2 to the n, and a gate that resets the chain early counts modulo n.
An astable's mark-to-space ratio is its high time over its low time; its duty cycle is its high time over the whole period.

Data communication

One modulating tone makes three frequencies, so AM occupies 2fM of spectrum while FM occupies 2(Δf + fM) and shrugs off amplitude noise.
Sample faster than twice the highest frequency, round to a level, send the code: PCM.
Ground wave hugs the surface, sky wave bends back off the ionosphere, space wave goes line of sight and on out to a satellite.
Fibre loses least and ignores interference; anything transmitted can be intercepted, so encryption and authentication have to ride in the data.

Engineering physicsYear 134 topics

Rotational motion and moment of inertia

Rotation reruns SUVAT with θ, ω and α standing in for s, v and a.
I sums mr² over the body, so distance from the axis counts squared.
A spinning store holds ½Iω², and the ω² makes spin rate worth more than mass.

Torque, angular momentum and rotational power

Torque is Fr, and it does for rotation what force does for a line: T = Iα.
No external torque means Iω is fixed, whatever internal rearranging happens.
Work is Tθ and power is Tω, the equations every engine question turns on.

The first law of thermodynamics

Q = ΔU + W, with W the work done by the gas: heat in becomes internal energy or work out.
Constant volume gives W = 0, isothermal gives ΔU = 0, adiabatic gives Q = 0.
On a p-V diagram, work is the area under the curve; pV is constant on an isotherm, pV^γ on a reversible adiabat of an ideal gas.

Heat engines and heat pumps

An engine taps the flow from hot to cold: W = Q_H − Q_C, rejecting Q_C is compulsory, and the ceiling is (T_H − T_C)/T_H in kelvin.
Four strokes and two revolutions make one cycle, and the area the indicator loop encloses is the work that cycle did.
Power audit: input from fuel, indicated in the cylinders, brake at the shaft, friction the gap; thermal times mechanical is overall.
Reversed, the cycle pumps heat uphill and its COP is the benefit over the work input, and rejected heat put to use is not wasted either.

AstrophysicsYear 137 topics

Telescopes and image formation

The objective makes a real image; the eye lens turns it into steeper parallel light.
In normal adjustment M is the objective's focal length over the eye lens's, and the tube is the two added.

Telescopes across the spectrum

θ ≈ λ over D, in radians, and smaller is sharper.
The light gathered grows as the diameter squared, so every extra metre counts four times over.
A CCD registers about 80 per cent of the photons that reach it. Your eye manages one.

Star brightness and magnitude

Magnitude runs backwards: smaller number, brighter star, 2.51 per step.
Absolute magnitude is the view from 10 parsecs; the distance modulus m − M gives d.

Black-body radiation and spectral classes

Wien reads the temperature off the peak of the curve.
Stefan turns temperature and area into power, and the fourth power dominates everything.
OBAFGKM files every star hot to cool.
Balmer lines peak at class A, because absorption needs atoms already sitting in n = 2.

The HR diagram and stellar evolution

The HR diagram maps brightness against temperature, hot on the left; only a magnitude scale runs backwards.
Sun-like stars end as white dwarfs, held up by electron degeneracy pressure below 1.4 solar masses.
Heavier stars die as core-collapse supernovae and leave a neutron star or a black hole.
A type Ia is a detonating white dwarf, standardised by its rate of decline.

The Doppler effect and Hubble's law

Away means red, towards means blue, and the fractional shift is the speed over c.
v = Hd turns a red shift into a distance, and 1/H clocks the whole universe.
The Cosmological principle: homogeneous, isotropic, and one set of physical laws everywhere.

Quasars and exoplanets

A quasar is an active supermassive black hole, giving galaxy power from a solar-system volume.
Its flicker time caps its size, and its red shift estimates its distance.
Exoplanets are found indirectly, by the star's Doppler wobble or by a transit dip of (rp/rs) squared.

Turning pointsYear 136 topics

Cathode rays and the electron

Cathode rays are electrons, boiled off a hot filament and accelerated by eV = ½mv².
Thomson measured e/m, about 1800 times the hydrogen ion's value.
Same charge, far less mass, so atoms must have smaller parts inside them.

Millikan's oil drop experiment

Hold the droplet still and QV/d = mg gives its charge. Let it fall and Stokes' law weighs it.
Every droplet carried a whole multiple of e, so free charge is quantised in units of the electronic charge.

The nature of light

Corpuscles need light faster in glass. Waves need it slower. The measured speed decides between them.
Young's dark fringes are two lights cancelling, which particles cannot do.
Maxwell computed c from two electrical constants, and light turned out to be his wave.
Hertz made those waves in a laboratory and measured their speed at c.

Quanta and wave-particle duality

Planck quantised energy at E = hf, and Einstein made the packets real as photons.
de Broglie reversed the idea with λ = h/p, and matter waves became microscopes.

The Michelson-Morley experiment

The most sensitive race of its age ended in a dead heat, to within its sensitivity, every time it was run, which killed absolute motion and left c invariant for every observer.

The consequences of special relativity

Moving clocks run slow and moving lengths shrink, by the same root, and the muons prove it.
Proper time is measured where both events happen in one place. Proper length is measured at rest with the object.
Mass grows with speed, E = mc² says by how much, and c is a limiting speed no amount of energy can reach.

Medical physicsYear 136 topics

Ultrasound imaging

Depth is ct over two, because the echo travelled there and back.
Impedance mismatch sets how much reflects, and the gel exists to remove the worst mismatch of all.
A-scan gives one line of depths. B-scan sweeps that line into a picture.
MR times how quickly tipped protons relax, and the relaxation time depends on the tissue: soft-tissue detail with no ionising dose.

X-rays and CT scanning

The tube pd caps the photon energy, so E max equals eV, and everything else in the beam is softer.
The smooth part of the spectrum is bremsstrahlung and stops at λ min = hc/eV; the sharp lines are characteristic of the target's own energy levels.
Attenuation is exponential, and contrast is a difference in μ between neighbouring tissues.
An intensifying screen lowers the dose at the expense of a little sharpness, and a flat panel reads the beam out as numbers.

Radionuclide imaging and PET

A tracer maps function, not shape, and the half-life that matters is the effective one: 1/T_E = 1/T_P + 1/T_B.
Photons have to be what leaves the patient. A gamma camera takes a gamma emitter; PET takes a positron emitter.
Annihilation gives two 511 keV photons back to back, and coincidence detection turns each pair into a line. The lines cross where the tracer is.
A beta-minus emitter cannot reach a gamma camera because its range is millimetres, and an implant treats for exactly that reason.

The physics of the eye

The image distance in the eye is fixed, so focusing changes the power, not the position of the lens.
Power in dioptres needs the focal length in metres, and a diverging lens has a negative power.
Myopia is a finite far point corrected by a diverging lens; hypermetropia is too little power for the eye's length, corrected by a converging lens. A distant near point with the far point still at infinity is lost accommodation, not long sight.
Cones give colour and detail in bright light; rods give sensitivity in the dark and lose the detail by sharing nerve fibres.

The physics of the ear

Intensity is power per unit area; intensity level is ten log of it against 1.0 × 10⁻¹² W m⁻².
The scale is logarithmic because the ear judges by ratio, so +10 dB is always ten times the intensity.
The middle ear raises the pressure by a lever and an area ratio, so the sound can get into the fluid of the cochlea.
Equal loudness curves dip near 3 kHz, flatten as they rise, and lift at the treble end when hearing is damaged.

Biological measurement

The ECG plots a potential difference at the skin, produced by the wave of depolarisation crossing the heart.
The amplifier needs high gain, high input impedance and low noise, and the electrodes need gel.
P is the atria depolarising, QRS the ventricles depolarising, T the ventricles repolarising.
QRS is the biggest because the ventricles carry the most muscle, and the R to R interval gives the rate.

Each links to its full lesson. See also command words and the revision checklist.