Free O Level Physics 5054 Study Guide — Edvia College
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O Level Physics 5054 — the whole syllabus, free.

A complete study guide for Cambridge O Level Physics 5054, mapped to all 25 sub-topics of the official syllabus for exams in 2026–2028, plus a full section on the experimental skills that carry 20% of your grade.

How to use it: physics rewards three separate things — knowing exact definitions, recalling equations (none are given to you), and applying both to unfamiliar situations. Each unit here gives you the definitions in examiner wording, the equations with units, a worked example, and a skill check. Do the skill check before opening the answer.

CAIE 5054 · exams 2026–202825 syllabus units6 topicsPractical/ATP includedFree & shareable
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The three papers

You sit three components: two theory papers everyone takes, plus one practical paper — either the real Practical Test (Paper 3) or the Alternative to Practical (Paper 4), depending on what your school enters you for.

PaperFormatTime / marksWeight
Paper 1 — Multiple Choice40 four-option multiple-choice questions1 hour · 40 marks30%
Paper 2 — TheoryShort-answer and structured questions1 h 45 min · 80 marks50%
Paper 3 — Practical Test orExperiments done in a laboratory1 h 30 min · 40 marks20%
Paper 4 — Alternative to PracticalWritten questions on experiments; no lab work1 hour · 40 marks20%

Assessment objectives: AO1 Knowledge with understanding 50%, AO2 Handling information and problem-solving 30%, AO3 Experimental skills 20%. Papers 3 and 4 are entirely AO3 — which is why the practical section of this guide matters as much as any topic.

A fifth of your grade is experimental skill, and it is the part most students revise least. If your school enters you for Paper 4 (Alternative to Practical), you still need to know how the experiments are actually done — the questions describe real apparatus and ask you to spot errors, suggest improvements and process data.
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Every equation you must recall

No formula sheet is provided in O Level Physics. Every equation below is one the syllabus says you must "recall and use" — if you cannot write it from memory, you cannot score the marks. This is the single highest-value page in the guide: learn it, test yourself weekly.

QuantityEquationUnits
Speedv = s / tm/s
Average speedtotal distance ÷ total timem/s
Accelerationa = Δv / Δtm/s²
Gravitational field strengthg = W / mN/kg (= m/s²)
WeightW = mgN
Densityρ = m / Vkg/m³ or g/cm³
Resultant forceF = maN
Spring constantk = F / xN/m
Moment of a forcemoment = F × perpendicular distance from pivotN m
Momentump = mvkg m/s
Impulseimpulse = FΔt = Δ(mv)N s
Force from momentumF = Δp / ΔtN
Kinetic energyEk = ½mv²J
Change in g.p.e.ΔEp = mgΔhJ
Work doneW = FdJ
Efficiencyuseful output ÷ total input (× 100%)— or %
PowerP = W / t = ΔE / tW
Pressurep = F / APa (N/m²)
Pressure in a liquidΔp = ρgΔhPa
Temperature conversionT (K) = θ (°C) + 273K
Specific heat capacityc = ΔE / (mΔθ)J/(kg °C)
Wave speedv = fλm/s
Refractive indexn = sin i / sin rno unit
Critical anglen = 1 / sin cno unit
Linear magnificationimage length ÷ object lengthno unit
Electric currentI = Q / tA
e.m.f.E = W / QV
Potential differenceV = W / QV
ResistanceR = V / IΩ
Resistors in seriesR = R₁ + R₂ + …Ω
Two resistors in parallel1/R = 1/R₁ + 1/R₂Ω
Potential dividerR₁ / R₂ = V₁ / V₂
Electrical powerP = IVW
Electrical energyE = IVtJ
TransformerVp / Vs = Np / Ns
Average orbital speedv = 2πr / Tm/s

Values worth knowing

  • g ≈ 9.8 N/kg (some questions use 10 N/kg — use the value the question gives)
  • Speed of all electromagnetic waves in a vacuum = 3.0 × 10⁸ m/s (air is approximately the same)
  • Speed of sound in air ≈ 330–350 m/s
  • Audible frequency range for humans: 20 Hz to 20 000 Hz; ultrasound is above 20 kHz
  • Water at standard atmospheric pressure: melts at 0 °C, boils at 100 °C
  • Light takes about 500 s to reach Earth from the Sun; Earth orbits in ≈365 days and spins in ≈24 hours
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Study planner & progress

All 25 syllabus units plus the practical skills section. Tick a unit when you can state its definitions from memory and answer a past-paper question on it. Your ticks are saved on this device only — nothing is sent anywhere, and there is no account to create.

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Topic 1 · 8 units

Motion, forces and energy

The biggest topic, and the foundation for everything else. Most of Paper 2's calculation marks live here, and almost every practical context (timing, springs, balances, density) comes from these units.

1.1Physical quantities and measurement techniques

Measuring length: tapes and rulers for larger lengths; a micrometer for small ones (you must be able to read an analogue micrometer scale). Volume: use a measuring cylinder for liquids, and displacement for an irregular solid that sinks — the rise in liquid level equals the solid's volume. Time: clocks and digital timers.

Method — measuring small quantities accuratelyMeasure a multiple and divide. For the thickness of one sheet of paper, measure 100 sheets and divide by 100. For the period of a pendulum, time 20 oscillations and divide by 20 — this reduces the effect of reaction-time error on each individual reading.
Scalars and vectorsA scalar has magnitude (size) only. A vector has magnitude and direction.
Scalars: distance, speed, time, mass, energy, temperature.
Vectors: displacement, force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength.
Worked example — resultant of two perpendicular vectors

A force of 3.0 N acts east and a force of 4.0 N acts north. Find the resultant.

  1. At right angles, use Pythagoras for the size: R = √(3.0² + 4.0²) = √25 = 5.0 N
  2. Direction from trigonometry: tan θ = 4.0/3.0 → θ = 53° north of east
  3. (Graphically: draw the two vectors to scale head-to-tail and measure the closing side.)
Giving a vector answer as a number only. If the question asks for a resultant vector, the direction is part of the answer and usually carries its own mark.
Skill check: A student times 20 swings of a pendulum as 31.4 s. Find the period, and explain why timing 20 swings is better than timing one.
Solution: Period = 31.4 ÷ 20 = 1.57 s. Timing 20 swings reduces the percentage uncertainty: the human reaction-time error (a few tenths of a second) is a much smaller fraction of 31.4 s than of 1.57 s, so dividing spreads that fixed error across many oscillations.

1.2Motion

Definitions — exact wordingSpeed is the distance travelled per unit time. Velocity is the change in displacement per unit time (a vector). Acceleration is the change in velocity per unit time.
v = s / t  ·  average speed = total distance ÷ total time  ·  a = Δv / Δt

A deceleration is a negative acceleration. Uniform acceleration means the velocity changes by equal amounts in equal times (e.g. free fall near Earth); non-uniform means it does not (e.g. a car in traffic).

Graph shapeDistance–time graphSpeed–time graph
Horizontal lineAt restConstant speed (zero acceleration)
Straight sloped lineConstant speedConstant acceleration
Curve getting steeperAcceleratingIncreasing acceleration
Curve getting shallowerDeceleratingDecreasing acceleration
Gradient givesSpeedAcceleration
Area under gives(no meaning)Distance travelled
Time / sSpeed / (m/s) 30 123242 a = 30/12 = 2.5 m/s² constant speed decelerating
Gradient = acceleration; shaded area = distance travelled.
Worked example

A car accelerates uniformly from rest to 30 m/s in 12 s, travels at 30 m/s for 20 s, then decelerates uniformly to rest in 10 s. Find (a) the acceleration in the first stage, (b) the total distance travelled.

  1. (a) a = Δv/Δt = (30 − 0)/12 = 2.5 m/s²
  2. (b) Area under a speed–time graph = distance:
  3. Triangle 1 = ½ × 12 × 30 = 180 m; rectangle = 20 × 30 = 600 m; triangle 2 = ½ × 10 × 30 = 150 m
  4. Total = 930 m
Skill check: An object in free fall accelerates at 9.8 m/s². Starting from rest, what is its speed after 3.0 s (ignoring air resistance)?
Solution: a = Δv/Δt, so Δv = a × Δt = 9.8 × 3.0 = 29.4 m/s (≈ 29 m/s).

1.3Mass and weight

DefinitionsMass is a measure of the quantity of matter in an object; it resists change from its state of rest or motion (inertia) and is the same everywhere. Weight is the gravitational force on an object — it changes with location. Gravitational field strength is force per unit mass, and equals the acceleration of free fall. A gravitational field is a region in which a mass experiences a force due to gravitational attraction.
g = W / m  ⟹  W = mg  (g ≈ 9.8 N/kg on Earth)

Measuring: mass with an electronic balance (or compare masses with a beam/equal-arm balance, since equal weights mean equal masses); weight with a force meter (spring balance) in newtons.

Worked example

A student has a mass of 60 kg. Find their weight on Earth (g = 9.8 N/kg) and on the Moon (g = 1.6 N/kg).

  1. Earth: W = 60 × 9.8 = 588 N
  2. Moon: W = 60 × 1.6 = 96 N
  3. The mass is 60 kg in both places — only the weight changes.
Writing weight in kilograms. Weight is a force, measured in newtons. "My weight is 60 kg" is everyday language, not physics.

1.4Density

DefinitionDensity is mass per unit volume.
ρ = m / V  (kg/m³ or g/cm³)
Method — measuring density
  • Liquid: find the mass of an empty measuring cylinder, add the liquid, find the new mass (subtract for the liquid's mass), read the volume directly.
  • Regular solid: mass on a balance; volume from measured dimensions.
  • Irregular solid that sinks: mass on a balance; volume by displacement — lower it into a measuring cylinder of water and record the rise in level.
Worked example

A stone of mass 240 g is lowered into a measuring cylinder containing 50 cm³ of water. The level rises to 80 cm³. Find the density of the stone in g/cm³ and in kg/m³.

  1. Volume = 80 − 50 = 30 cm³
  2. ρ = 240 ÷ 30 = 8.0 g/cm³
  3. Convert: 1 g/cm³ = 1000 kg/m³, so ρ = 8000 kg/m³
Density is a favourite practical context. Expect to be asked why you should dry the object before massing it, why the cylinder must be read at eye level (avoiding parallax error) and how repeating improves reliability.
Skill check: An object floats in water (density 1.0 g/cm³). What can you say about its density, and why?
Solution: Its density is less than 1.0 g/cm³. An object floats when it is less dense than the fluid — it can displace a weight of water equal to its own weight before becoming fully submerged.

1.5Forces

1.5.1 Balanced and unbalanced forces. Types of force to know: weight (gravitational), friction, drag, air resistance, tension (elastic), electrostatic, magnetic, thrust (driving) and contact force. You must be able to draw free-body diagrams showing the forces on one object.

Newton's laws — state them exactly First law: an object either remains at rest or continues to move in a straight line at constant speed unless acted on by a resultant force.
Second law (as an equation): resultant force = mass × acceleration.
Third law: when object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These pairs are the same type of force acting on different objects.
F = ma
Worked example

A car of mass 1200 kg experiences a resultant forward force of 3600 N. Find its acceleration.

  1. a = F/m = 3600 ÷ 1200 = 3.0 m/s²

1.5.2 Friction. Friction is a force that may impede motion and produce heating. With a constant driving force, an object speeds up until drag (air resistance) grows equal to the driving force — then the resultant force is zero and it moves at constant terminal velocity.

Stopping distanceThinking distance is the distance travelled during the driver's reaction time; braking distance is the distance travelled while braking; stopping distance = thinking + braking distance.
Thinking distance increases with speed, tiredness, alcohol and drugs. Braking distance increases with speed, load, worn tyres and wet or icy road conditions.

1.5.3 Elastic deformation. Forces can change an object's size and shape.

DefinitionSpring constant is force per unit extension. The limit of proportionality is the point on a load–extension graph beyond which extension is no longer proportional to load — the graph stops being a straight line.
k = F / x  (N/m)
Worked example

A spring extends by 4.0 cm when a 6.0 N load is hung on it, within the limit of proportionality. Find the spring constant, and the extension caused by a 9.0 N load.

  1. Convert: 4.0 cm = 0.040 m
  2. k = 6.0 ÷ 0.040 = 150 N/m
  3. For 9.0 N: x = F/k = 9.0 ÷ 150 = 0.060 m = 6.0 cm
The load–extension experiment is a classic P3/P4 context. Key points: measure the unloaded length first and always subtract it (extension ≠ length), add loads in equal steps, check the spring returns to its original length, and read the ruler at eye level against a fixed pointer.

1.5.4 Circular motion. An object moves in a circle because a force acts perpendicular to its motion. Qualitatively: with mass and radius constant, a bigger force means a bigger speed; with mass and speed constant, a bigger force means a smaller radius; a bigger mass needs a bigger force for the same speed and radius. (The equation F = mv²/r is not required.)

1.5.5 Turning effect of forces.

DefinitionsThe moment of a force is a measure of its turning effect: moment = force × perpendicular distance from the pivot (N m).
Principle of moments: for an object in equilibrium, the sum of the clockwise moments about a pivot equals the sum of the anticlockwise moments.
Worked example

A uniform beam balances on a pivot. A 3.0 N weight sits 0.40 m to the left of the pivot. At what distance to the right must a 4.8 N weight be placed to balance it?

  1. Anticlockwise moment = 3.0 × 0.40 = 1.2 N m
  2. For equilibrium, clockwise moment = 1.2 N m = 4.8 × d
  3. d = 1.2 ÷ 4.8 = 0.25 m

1.5.6 Centre of gravity. The centre of gravity is the point at which the whole weight of an object may be considered to act. Find it for a plane lamina by hanging it freely from two or three different points and drawing a plumb line each time — the lines cross at the centre of gravity. An object is more stable when its centre of gravity is low and its base is wide, because it must be tilted further before its line of action of weight falls outside the base.

Skill check: A skydiver falls at terminal velocity, then opens a parachute. Explain, in terms of forces, what happens next.
Solution: At terminal velocity, weight = drag, so the resultant force is zero and speed is constant. Opening the parachute greatly increases the surface area, so drag becomes larger than weight — there is now an upward resultant force, so the skydiver decelerates. As speed falls, drag falls, until drag again equals weight and a new, lower terminal velocity is reached.

1.6Momentum

DefinitionsMomentum = mass × velocity (a vector, kg m/s). Impulse = force × time for which the force acts. Resultant force is the change in momentum per unit time.
p = mv  ·  impulse = FΔt = Δ(mv)  ·  F = Δp / Δt
Principle of conservation of momentumIn a collision or explosion, the total momentum before = total momentum after, provided no external force acts. Take one direction as positive and give opposite motion a negative sign.
Worked example

A trolley of mass 2.0 kg moving at 3.0 m/s collides with a stationary 1.0 kg trolley and they stick together. Find their common velocity afterwards.

  1. Momentum before = (2.0 × 3.0) + (1.0 × 0) = 6.0 kg m/s
  2. After, combined mass = 3.0 kg moving at v: momentum = 3.0v
  3. Conservation: 3.0v = 6.0 → v = 2.0 m/s in the original direction
Momentum explains car safety features: crumple zones, airbags and seatbelts all increase the time over which momentum changes. Since F = Δp/Δt, a larger Δt for the same Δp means a smaller force on the passenger. Say it in exactly that way and the marks follow.
Skill check: A 0.15 kg ball travelling at 20 m/s is struck and rebounds at 25 m/s in the opposite direction. Find the change in momentum.
Solution: Take the initial direction as positive. Initial p = 0.15 × 20 = 3.0 kg m/s; final p = 0.15 × (−25) = −3.75 kg m/s. Change = −3.75 − 3.0 = −6.75 kg m/s, i.e. a magnitude of 6.75 kg m/s in the rebound direction. (Forgetting the sign change gives 0.75 — the classic error.)

1.7Energy, work and power

1.7.1 Energy stores: kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic and internal (thermal). Energy is transferred between stores by forces (mechanical work), electrical currents (electrical work), heating, and by electromagnetic, sound and other waves.

Principle of conservation of energyEnergy cannot be created or destroyed; it can only be transferred from one store to another, and the total energy of a closed system is constant.
Ek = ½mv²  ·  ΔEp = mgΔh  ·  W = Fd  ·  P = W/t = ΔE/t
Worked example — energy transfer

A 2.0 kg ball is dropped from a height of 5.0 m (g = 9.8 N/kg). Ignoring air resistance, find its speed just before it lands.

  1. Loss in g.p.e. = mgΔh = 2.0 × 9.8 × 5.0 = 98 J
  2. All of this becomes kinetic energy: ½mv² = 98
  3. ½ × 2.0 × v² = 98 → v² = 98 → v = 9.9 m/s

1.7.3 Energy resources. Know how useful energy or electrical power is obtained from: fossil fuels, biofuels, hydroelectric, solar, nuclear, geothermal, wind, tides and waves — referring to a boiler, turbine and generator where used. Compare them on whether they are renewable, when/whether they are available, and their environmental impact.

ResourceRenewable?Key advantageKey disadvantage
Fossil fuelsNoReliable, high energy output on demandCO₂ and pollutants; will run out
Nuclear fuelNoNo CO₂ in operation; very large outputRadioactive waste; high cost; accident risk
SolarYesNo fuel cost or emissions in useOnly in daylight; weather-dependent
WindYesNo emissions in useOnly when windy; visual/noise impact
HydroelectricYesReliable; can respond quickly to demandNeeds suitable valley; flooding of land/habitats
GeothermalYesAvailable continuouslyOnly in suitable locations
Tides / wavesYesPredictable (tides); no emissionsLimited sites; damage to coastal habitats
Efficiencyefficiency = useful energy output ÷ total energy input (× 100%), or equivalently useful power output ÷ total power input.
Worked example

A motor is supplied with 1600 J of electrical energy and does 400 J of useful work. Find its efficiency, and state what happens to the rest.

  1. Efficiency = 400 ÷ 1600 = 0.25 = 25%
  2. The other 1200 J is transferred to the surroundings, mostly as internal (thermal) energy because of friction, and some as sound.
Worked example — power

A crane lifts a 500 N load through 6.0 m in 10 s. Find the work done and the useful power output.

  1. W = Fd = 500 × 6.0 = 3000 J
  2. P = W/t = 3000 ÷ 10 = 300 W
Using the total distance moved rather than the distance moved in the direction of the force in W = Fd. Carrying a bag horizontally does no work against gravity, because the weight acts downwards and the movement is sideways.
Skill check: Find the kinetic energy of a 60 kg runner moving at 8.0 m/s.
Solution: Ek = ½ × 60 × 8.0² = ½ × 60 × 64 = 1920 J (≈ 1.9 kJ). Note the speed is squared — doubling speed quadruples kinetic energy, which is why braking distance grows so fast with speed.

1.8Pressure

DefinitionPressure is force per unit area. The pressure at a surface produces a force at right angles to that surface.
p = F / A  (Pa = N/m²)  ·  Δp = ρgΔh

Everyday consequences: a sharp knife has a very small area so the same force gives a very large pressure; a camel's wide foot or a tractor's wide tyres spread weight over a large area, reducing pressure so it does not sink.

In a liquid, pressure increases with depth and with the density of the liquid. A liquid barometer uses the height of a liquid column that atmospheric pressure can support to measure that atmospheric pressure.

Worked example

(a) A box weighing 600 N rests on an area of 0.15 m². Find the pressure. (b) Find the extra pressure 20 m below the surface of water (ρ = 1000 kg/m³, g = 9.8 N/kg).

  1. (a) p = 600 ÷ 0.15 = 4000 Pa
  2. (b) Δp = ρgΔh = 1000 × 9.8 × 20 = 196 000 Pa (1.96 × 10⁵ Pa)
Skill check: Why do dam walls get thicker towards the bottom?
Solution: Pressure in a liquid increases with depth (Δp = ρgΔh), so the water pushes hardest at the base of the dam. The wall must be thicker there to withstand the greater force.
Topic 2 · 3 units

Thermal physics

Nearly every mark here comes from explaining things in terms of particles. Train yourself to answer with the same three variables every time: the particles' spacing, their arrangement, and their motion (speed/kinetic energy).

2.1Kinetic particle model of matter

SolidLiquidGas
SpacingVery closeCloseFar apart
ArrangementRegular, fixed latticeRandom, but touchingRandom, spread out
MotionVibrate about fixed positionsMove around each otherMove rapidly in all directions
Forces betweenStrongWeakerNegligible
PropertiesFixed shape and volumeFixed volume, takes shape of containerNo fixed shape or volume; compressible

Changes of state: melting (solid→liquid), solidification/freezing (liquid→solid), boiling and evaporation (liquid→gas), condensation (gas→liquid). Gas↔solid transfers are not required.

Gas behaviour — the particle explanationPressure is caused by gas particles colliding with the container walls; each collision exerts a small force.
Increase temperature at constant volume → particles move faster, hit the walls harder and more often → pressure increases.
Decrease volume at constant temperature → particles hit the walls more often (same speed, smaller space) → pressure increases.

Brownian motion: smoke particles viewed under a microscope move in random, jerky paths because they are bombarded unevenly by fast-moving, invisible air molecules — direct evidence for the particle model.

Skill check: Explain, in terms of particles, why a gas is easy to compress but a liquid is not.
Solution: In a gas, particles are far apart with large spaces between them, so they can be pushed much closer together. In a liquid the particles are already touching, so there is very little space to remove — strong repulsion at close range resists further compression.

2.2Thermal properties and temperature

2.2.1 Thermal expansion. Heating makes particles vibrate/move more and take up more space, so materials expand. Order of expansion for the same temperature rise: gases > liquids > solids. Applications and consequences: the liquid-in-glass thermometer (liquid expands up a narrow tube), expansion gaps in bridges and railway lines, and bimetallic strips.

T (in K) = θ (in °C) + 273

2.2.2 Specific heat capacity. Raising an object's temperature increases its internal energy — specifically the average kinetic energy of all its particles.

DefinitionSpecific heat capacity is the energy required per unit mass per unit temperature increase.
c = ΔE / (mΔθ)  ⟹  ΔE = mcΔθ
Worked example

9000 J of energy raises the temperature of a 0.50 kg metal block by 20 °C. Find its specific heat capacity.

  1. c = ΔE ÷ (mΔθ) = 9000 ÷ (0.50 × 20)
  2. = 9000 ÷ 10 = 900 J/(kg °C)
A specific heat capacity experiment (immersion heater in a metal block, thermometer, and joulemeter or ammeter+voltmeter+timer) is a common P3/P4 context. The measured value is usually too high because some energy is transferred to the surroundings and to the container — insulating the block is the standard improvement to suggest.

2.2.3 Melting, boiling and evaporation. During melting, solidification, boiling and condensation, energy is transferred without a change in temperature — this is latent heat, the energy required to change the state of a substance. It goes into breaking (or forming) the forces between particles rather than speeding them up. For water at standard atmospheric pressure: melting point 0 °C, boiling point 100 °C.

BoilingEvaporation
Happens at one fixed temperatureHappens at any temperature below boiling point
Occurs throughout the liquid (bubbles)Occurs only at the surface
Relatively fastRelatively slow

Evaporation is the escape of the more energetic particles from the surface of a liquid. It is faster at higher temperature, with larger surface area, and with air movement over the surface. It causes cooling because the particles left behind have a lower average kinetic energy — and average kinetic energy is what temperature measures.

Skill check: Explain why you feel cold when you step out of a swimming pool on a windy day.
Solution: Water on your skin evaporates. The most energetic water molecules escape first, so the average kinetic energy of those remaining falls — the water (and your skin) cools. Wind removes the evaporated molecules from above the surface, so evaporation continues faster, increasing the cooling.

2.3Transfer of thermal energy

ProcessHow it worksWhere it occurs
ConductionLattice vibrations pass energy between neighbouring atoms; in metals, free (delocalised) electrons also carry energy — which is why metals conduct so much betterMainly solids
ConvectionHeated fluid expands, becomes less dense, rises; cooler denser fluid sinks to replace it, forming a convection currentLiquids and gases only
RadiationEmission of infrared electromagnetic waves; requires no medium — it works through a vacuumEverywhere, including space

Surfaces and radiation: dull black surfaces are the best emitters and best absorbers; shiny white/silver surfaces are the poorest emitters and absorbers, and the best reflectors. The rate of emission increases with higher surface temperature and larger surface area.

Everyday applications: metal pans conduct heat quickly to food; a room heater warms a room by convection currents; an infrared thermometer detects emitted radiation to measure temperature without contact; a vacuum flask and building insulation reduce all three transfers (vacuum stops conduction and convection; silvered surfaces reduce radiation).

Skill check: Explain why the heating element in an electric kettle is placed at the bottom.
Solution: Water heated at the bottom expands, becomes less dense and rises; cooler, denser water sinks to take its place, setting up a convection current that heats all the water. If the element were at the top, the hot water would stay there (already less dense) and the rest would heat only slowly by conduction, which is poor in water.
Topic 3 · 4 units

Waves

Light and sound both reduce to the same small set of ideas, plus ray diagrams you must be able to draw accurately with a ruler. Refraction and total internal reflection are the highest-yield calculations in this topic.

3.1General properties of waves

Key idea and definitionsWaves transfer energy without transferring matter.
Frequency is the number of wavelengths that pass a point per unit time (Hz).
Wavelength is the distance between two consecutive identical points, such as two consecutive crests (m).
Amplitude is the maximum distance from the mean position (m).
v = fλ  (wave speed = frequency × wavelength)
Transverse waveLongitudinal wave
Vibration is at right angles to the direction of energy transferVibration is parallel to the direction of energy transfer
Examples: electromagnetic radiation, water surface waves, seismic S-waves (secondary)Examples: sound waves, seismic P-waves (primary)

Wave behaviours: reflection at a plane surface (wave bounces back, speed and wavelength unchanged); refraction due to a change of speed (in a ripple tank, caused by a change in water depth); diffraction through a gap or at an edge (waves spread out). Diffraction is greatest when the gap size is similar to the wavelength; a wide gap causes little spreading, and longer wavelengths diffract more at an edge.

The ripple tank is the standard demonstration apparatus: a plane barrier shows reflection, a shallow region (a glass plate under the water) shows refraction, and gaps or edges in barriers show diffraction.
Worked example

A water wave has a frequency of 50 Hz and a wavelength of 6.0 m. Find its speed.

  1. v = fλ = 50 × 6.0 = 300 m/s
Skill check: A radio station broadcasts at 90 MHz. Find the wavelength (speed of radio waves = 3.0 × 10⁸ m/s).
Solution: λ = v/f = (3.0 × 10⁸) ÷ (90 × 10⁶) = 3.3 m (2 s.f.).

3.2Light

3.2.1 Reflection. The normal is the line drawn at right angles to the surface at the point where the ray strikes. The angle of incidence and angle of reflection are both measured from the normal.

Law of reflectionThe angle of incidence = the angle of reflection.
An image in a plane mirror is: the same size as the object, the same distance behind the mirror as the object is in front, laterally inverted, and virtual.

3.2.2 Refraction. Light changes speed when it enters a different medium, so it changes direction (unless it enters along the normal).

n = sin i / sin r  ·  n = 1 / sin c
DefinitionsThe critical angle c is the angle of incidence in the denser medium for which the angle of refraction is 90°. Total internal reflection occurs when light travelling in a denser medium strikes the boundary at an angle of incidence greater than the critical angle — all the light is reflected back inside.
normal i r air (less dense) glass (denser)
Entering a denser medium, light slows and bends towards the normal, so r < i. Leaving into a less dense medium it bends away from the normal.
Worked example

Light enters glass from air with an angle of incidence of 45° and an angle of refraction of 28°. Find (a) the refractive index, (b) the critical angle for this glass.

  1. (a) n = sin 45° ÷ sin 28° = 0.7071 ÷ 0.4695 = 1.5
  2. (b) sin c = 1/n = 1/1.5 = 0.667
  3. c = sin⁻¹(0.667) = 41.8°

Optical fibres use total internal reflection to carry light signals along a curved path. In telecommunications this gives very high data rates, low signal loss over long distances, immunity to electrical interference, and cables that are thinner and lighter than copper.

3.2.3 Thin lenses. A converging (convex) lens brings a parallel beam to a focus; a diverging (concave) lens spreads a parallel beam out. The principal axis is the line through the centre of the lens perpendicular to it; the principal focus (focal point) is where rays parallel to the principal axis converge; the focal length is the distance from the lens to the principal focus.

Real vs virtual imagesA real image is formed by converging rays and can be projected onto a screen. A virtual image is formed by diverging rays and cannot be projected.
linear magnification = image length ÷ object length
Method — drawing ray diagrams for a converging lensDraw any two of these three standard rays from the top of the object:
  1. A ray parallel to the principal axis, which refracts through the principal focus.
  2. A ray through the centre of the lens, which continues straight on.
  3. A ray through the principal focus on the object side, which refracts parallel to the axis.
Where they meet is the top of the image. Use a ruler and mark the arrow directions.

Magnifying glass: a single converging lens with the object placed closer than the focal length gives an enlarged, upright, virtual image.

Eye defects: a short-sighted eye focuses distant objects in front of the retina — corrected with a diverging lens. A long-sighted eye focuses near objects behind the retina — corrected with a converging lens.

3.2.4 Dispersion. A glass prism refracts white light by different amounts for different colours, splitting it into a spectrum. The seven traditional colours in order are red, orange, yellow, green, blue, indigo, violet — red has the longest wavelength and lowest frequency; violet has the shortest wavelength and highest frequency.

Skill check: A glass block has a critical angle of 42°. Light inside the glass strikes the boundary with air at 50°. What happens?
Solution: 50° is greater than the critical angle of 42°, so the light undergoes total internal reflection — none of it emerges into the air; it all reflects back into the glass, obeying the law of reflection.

3.3Electromagnetic spectrum

All electromagnetic waves are transverse, travel at 3.0 × 10⁸ m/s in a vacuum (approximately the same in air), and can travel through a vacuum.

Region (increasing frequency →)Uses
Radio waves (longest λ, lowest f)Radio and television communications, astronomy
MicrowavesSatellite television, mobile (cell) phones, Bluetooth, microwave ovens
InfraredHousehold electrical appliances, remote controllers, intruder alarms, thermal imaging, optical fibres
Visible lightPhotography, vision
UltravioletSecurity marking, detecting counterfeit banknotes, sterilising water
X-raysMedical imaging, security scanners, killing cancerous cells, detecting cracks in metal
Gamma rays (shortest λ, highest f)Detecting and killing cancerous cells, sterilising food and medical equipment, detecting cracks in metal

Damage: excessive exposure heats soft tissues and causes burns. Ionising effects come from ultraviolet (skin cancer, cataracts), X-rays and gamma rays (cell mutation and cancer).

Remember the order with any mnemonic you like, but be sure you can state it both ways — increasing frequency and increasing wavelength are opposite orders, and questions specify which one they want.

3.4Sound

Sound is produced by vibrating sources and travels as a longitudinal wave made of compressions (particles pushed together, high pressure) and rarefactions (particles spread apart, low pressure).

  • Sound cannot travel through a vacuum because it needs particles to transmit the vibrations. Demonstration: a ringing electric bell inside a bell jar becomes inaudible as the air is pumped out, though it can still be seen vibrating.
  • Human audible range: 20 Hz to 20 000 Hz. Ultrasound is sound above 20 kHz.
  • Greater amplitude → louder sound. Greater frequency → higher pitch. Different sources give different qualities (timbres), seen as different waveform shapes on an oscilloscope.
  • Speed of sound in air ≈ 330–350 m/s. In general sound travels faster in solids than liquids, and faster in liquids than gases (particles are closer, so vibrations pass on more quickly).
  • An echo is the reflection of sound waves.
Method — echo and sonar calculationsThe sound travels to the reflector and back, so the distance it covers is twice the distance to the object:
distance to object = (speed × time) ÷ 2
Worked example

A ship's sonar sends an ultrasound pulse into the sea and detects the echo from the seabed 0.30 s later. The speed of sound in seawater is 1500 m/s. Find the depth.

  1. Total distance travelled = 1500 × 0.30 = 450 m
  2. This is down and back, so depth = 450 ÷ 2 = 225 m

Uses of ultrasound: cleaning delicate objects, prenatal and other medical scanning, and sonar for measuring depth or locating objects.

To measure the speed of sound in air: stand a measured distance from a large wall, clap and time (say) 20 echoes with a stopwatch, then use speed = (2 × distance × 20) ÷ total time. Timing many echoes reduces the percentage uncertainty from reaction time.
Skill check: A person hears an echo from a cliff 1.6 s after shouting. If the speed of sound is 340 m/s, how far away is the cliff?
Solution: Total distance = 340 × 1.6 = 544 m. That is there and back, so distance to cliff = 544 ÷ 2 = 272 m.
Topic 4 · 6 units

Electricity and magnetism

The second-biggest topic and the one with the most circuit calculations. Get comfortable with the three-step routine for any circuit: find the total resistance, then the total current, then work back to individual components.

4.1Simple magnetism and magnetic fields

  • Like poles repel, unlike poles attract. A magnet also attracts unmagnetised magnetic materials (iron, steel, cobalt, nickel) by induced magnetism — the material becomes a magnet while in the field.
  • A magnetic field is a region in which a magnetic pole experiences a force. Its direction at a point is the direction of the force on a north pole placed there, so field lines run from N to S outside a magnet.
  • Field strength is shown by the spacing of the field lines — closer lines mean a stronger field.
  • Plotting fields: with a plotting compass (mark the needle's direction at successive points) or by sprinkling iron filings.
Temporary magnet (soft iron)Permanent magnet (steel)
MagnetisedEasilyWith difficulty
Keeps magnetismLoses it easilyRetains it
Used forElectromagnet cores, relays, transformer coresCompass needles, loudspeakers, fridge magnets, motors

4.2Electrical quantities

4.2.1 Charge. Charge is positive or negative, measured in coulombs (C). Unlike charges attract, like charges repel. Charging a solid by friction involves the transfer of negative charge (electrons) only — rub a polythene rod with a cloth and electrons move onto the rod, leaving the cloth positive. An electric field is a region in which a charge experiences a force; the field direction is the direction of the force on a positive charge.

Conductors (metals, graphite) have free electrons that can move through the material; insulators (plastic, glass, rubber) have electrons bound to atoms and cannot conduct.

4.2.2 Current.

DefinitionElectric current is the charge passing a point per unit time. Measured in amps; 1 A = 1 coulomb per second (C/s).
I = Q / t

In metals, current is the movement of free electrons. Conventional current flows from positive to negative; the free electrons actually flow from negative to positive. d.c. flows in one direction only; a.c. repeatedly reverses direction. Ammeters are connected in series.

4.2.3 e.m.f. and p.d.

Definitions — these two are frequently confusede.m.f. is the electrical work done by a source in moving a unit charge around a complete circuit.
p.d. is the work done by a unit charge passing through a component.
E = W / Q  ·  V = W / Q  (both in volts; 1 V = 1 J/C)

Voltmeters are connected in parallel across the component.

4.2.4 Resistance.

R = V / I  (ohms, Ω)
Ohm's lawThe current through a metallic conductor is directly proportional to the potential difference across it, provided the temperature remains constant.

For a wire: resistance is directly proportional to length and inversely proportional to cross-sectional area — a longer, thinner wire has more resistance.

ComponentShape of I–V graphWhy
Fixed resistor (constant temperature)Straight line through the originConstant resistance — obeys Ohm's law
Filament lampCurve that flattens as V increasesCurrent heats the filament; ions vibrate more, so resistance increases
DiodeCurrent only in one direction (forward); almost none in reverseVery high resistance in the reverse direction
Worked example

(a) A charge of 60 C passes a point in 20 s. Find the current. (b) A 12 V supply drives 0.50 A through a resistor. Find its resistance.

  1. (a) I = Q/t = 60 ÷ 20 = 3.0 A
  2. (b) R = V/I = 12 ÷ 0.50 = 24 Ω

4.3Electric circuits

You must be able to draw and interpret circuit diagrams containing cells, batteries, power supplies, generators, oscilloscopes, potential dividers, switches, fixed and variable resistors, heaters, thermistors (NTC), LDRs, lamps, motors, ammeters, voltmeters, magnetising coils, transformers, fuses, relays, diodes and LEDs.

Series and parallel — the four facts
  1. Current is the same at every point in a series circuit.
  2. At a junction, the currents in equal the currents out.
  3. In series, the supply p.d. is shared: total p.d. = sum of individual p.d.s.
  4. In parallel, each branch has the same p.d. across it.
Series: R = R₁ + R₂ + …  ·  Parallel (two resistors): 1/R = 1/R₁ + 1/R₂
Worked example

A 6.0 Ω and a 3.0 Ω resistor are connected in parallel across a 12 V supply. Find (a) the combined resistance, (b) the total current, (c) the current in the 6.0 Ω resistor.

  1. (a) 1/R = 1/6.0 + 1/3.0 = 1/6 + 2/6 = 3/6 → R = 2.0 Ω
  2. (b) I = V/R = 12 ÷ 2.0 = 6.0 A
  3. (c) Each branch has the full 12 V across it: I = 12 ÷ 6.0 = 2.0 A (the 3.0 Ω branch carries 4.0 A; 2.0 + 4.0 = 6.0 A ✓)
Adding parallel resistances like series ones. Two resistors in parallel always give a combined resistance smaller than either one — if your answer is bigger, you have made an error. Also remember to invert at the end: 1/R = 0.5 means R = 2, not 0.5.

4.3.3 Input sensors and potential dividers. An NTC thermistor's resistance decreases as temperature increases. An LDR's resistance decreases as light intensity increases. Both are used as input sensors in potential divider circuits — as their resistance changes, the share of the supply voltage across them changes, which can switch a circuit on or off (fire alarms, automatic lighting).

R₁ / R₂ = V₁ / V₂
Skill check: Two resistors, 4.0 Ω and 8.0 Ω, are in series across a 6.0 V supply. Find the current and the p.d. across the 8.0 Ω resistor.
Solution: Total R = 4.0 + 8.0 = 12 Ω. Current I = V/R = 6.0 ÷ 12 = 0.50 A (the same everywhere in series). p.d. across the 8.0 Ω = IR = 0.50 × 8.0 = 4.0 V. (Check: the 4.0 Ω has 2.0 V, and 2.0 + 4.0 = 6.0 V ✓)

4.4Practical electricity

P = IV  ·  E = IVt

Common uses of electricity: heating, lighting, battery charging, powering motors and electronic systems. Lamps are connected in parallel in a lighting circuit so that each gets the full mains voltage, each can be switched independently, and one failing does not break the others' circuit.

The kilowatt-hour1 kW h is the energy transferred by a 1 kW appliance in 1 hour. cost = number of kW h × cost per kW h.
Worked example

A 2.0 kW heater runs for 3.0 hours. Electricity costs 25 rupees per kW h. Find the energy used in kW h and the cost.

  1. Energy = power × time = 2.0 × 3.0 = 6.0 kW h
  2. Cost = 6.0 × 25 = 150 rupees

4.4.2 Electrical safety. Hazards: damaged insulation, overheating cables, damp conditions, and excess current from overloading plugs, extension leads and sockets.

  • A fuse is a thin wire that melts and breaks the circuit if the current exceeds its rating; a trip switch (circuit breaker) does the same job automatically and can be reset. Choose a rating just above the appliance's normal operating current.
  • Fuses and switches must be in the live wire, so that when they break the circuit the appliance is isolated from the high voltage. A switch in the neutral wire would stop the current but leave the appliance at live potential — still dangerous.
  • The mains has a live (line), neutral and earth wire. If a live wire touches an earthed metal case, a very large current flows to earth, which blows the fuse and disconnects the supply — preventing the case from becoming live.
  • An appliance's outer casing must be either earthed or non-conducting (double-insulated).
Worked example — choosing a fuse

A 230 V appliance is rated at 1000 W. Which fuse should be fitted: 3 A, 5 A or 13 A?

  1. I = P/V = 1000 ÷ 230 = 4.35 A
  2. The fuse must be above the normal current but as low as possible → 5 A
Skill check: A 12 V motor draws 2.5 A. Find its power and the energy transferred in 4.0 minutes.
Solution: P = IV = 2.5 × 12 = 30 W. Time must be in seconds: 4.0 min = 240 s. E = Pt = 30 × 240 = 7200 J (7.2 kJ).

4.5Electromagnetic effects

4.5.1 Electromagnetic induction. When a conductor cuts magnetic field lines (or the field through a coil changes), an e.m.f. is induced. The induced e.m.f. is larger with a faster movement, a stronger magnetic field, or more turns on the coil.

Lenz's lawThe effect of the current produced by an induced e.m.f. is to oppose the change producing it.

4.5.2 The a.c. generator. A coil rotating in a magnetic field (or a rotating magnet) induces an alternating e.m.f., taken off through slip rings and brushes. The e.m.f. is maximum when the coil is parallel to the field lines (cutting them fastest) and zero when it is perpendicular to them (moving along the lines, cutting none).

4.5.3 Magnetic effect of a current. A current in a straight wire produces circular field lines around it; a solenoid produces a field like a bar magnet's, strong and uniform inside. Increasing the current strengthens the field; reversing the current reverses the field direction. Used in relays (a small current switches a larger circuit) and loudspeakers (varying current in a coil in a magnetic field moves the cone to produce sound).

4.5.4 Force on a current-carrying conductor. A wire carrying a current in a magnetic field experiences a force (the motor effect). Reversing either the current or the field reverses the force; reversing both leaves it unchanged. Force, field and current are mutually perpendicular.

4.5.5 The d.c. motor. A current-carrying coil in a magnetic field experiences a turning effect, increased by more turns, a larger current, or a stronger field. The split-ring commutator reverses the current in the coil every half turn, so the coil keeps rotating in the same direction rather than stopping in a vertical position.

4.5.6 The transformer. An alternating current in the primary coil produces a changing magnetic field in the soft-iron core, which induces an alternating e.m.f. in the secondary coil. Step-up transformers increase voltage (more turns on the secondary); step-down decrease it.

Vp / Vs = Np / Ns
Worked example

A transformer has 1000 turns on the primary and 50 turns on the secondary. The primary is connected to 240 V a.c. Find the secondary voltage, and state the type of transformer.

  1. Vs = Vp × Ns/Np = 240 × 50/1000
  2. = 12 V — a step-down transformer (fewer secondary turns)
Why high-voltage transmission? Power loss in cables is caused by their resistance and equals I²R. For a given power transmitted (P = IV), a higher voltage means a smaller current, and because the loss depends on the current squared, halving the current quarters the wasted power. Say "less current, so less energy wasted as heat in the cables" for the mark.
Skill check: A transformer steps 240 V down to 6.0 V. If the primary has 800 turns, how many turns has the secondary?
Solution: Ns = Np × Vs/Vp = 800 × 6.0/240 = 20 turns.

4.6Uses of an oscilloscope

An oscilloscope displays waveforms (you do not need to know its internal structure). It can measure p.d. and short time intervals.

Method — reading an oscilloscope trace
  • Y-gain (volts per division): p.d. = number of vertical divisions × Y-gain setting.
  • Timebase (time per division): time = number of horizontal divisions × timebase setting. For a wave, measure the divisions for one complete cycle to get the period T, then frequency f = 1/T.
Worked example

A trace shows one complete wave across 4.0 horizontal divisions with the timebase set to 5.0 ms per division. The peak reaches 3.0 vertical divisions with the Y-gain at 2.0 V per division. Find the period, frequency and peak voltage.

  1. Period T = 4.0 × 5.0 ms = 20 ms = 0.020 s
  2. Frequency f = 1/T = 1 ÷ 0.020 = 50 Hz
  3. Peak p.d. = 3.0 × 2.0 = 6.0 V
Topic 5 · 2 units

Nuclear physics

Small topic, very predictable questions: nuclide notation, decay equations, the three radiations compared, half-life calculations, and safety. Learn the comparison table cold and you have most of the marks.

5.1The nuclear model of the atom

5.1.1 The atom. An atom has a positively charged nucleus with negatively charged electrons in orbit around it.

Alpha-particle scattering — the evidenceAlpha particles fired at thin gold foil gave three observations, each with a conclusion:
  • Most passed straight through → the atom is mostly empty space.
  • A few were deflected through large angles → the nucleus is positively charged (repelling the positive alpha particles).
  • Very few bounced almost straight back → the nucleus is very small and contains most of the mass.

5.1.2 The nucleus. The nucleus contains protons and neutrons. Atoms form positive ions by losing electrons and negative ions by gaining electrons.

NotationProton number (atomic number) Z = number of protons. Nucleon number (mass number) A = number of protons + neutrons.
Number of neutrons = AZ. A nuclide is written AZX.
Isotopes are atoms of the same element with the same proton number but different numbers of neutrons.
Worked example

For the nuclide 23892U, state the number of protons, neutrons and electrons in a neutral atom.

  1. Protons = Z = 92
  2. Neutrons = AZ = 238 − 92 = 146
  3. Electrons in a neutral atom = protons = 92

5.2Radioactivity

5.2.1 Detection. Alpha particles can be detected with a cloud chamber or spark counter; beta particles and gamma radiation with a Geiger-Müller tube and counter. Count rate is measured in counts/s or counts/minute.

Background radiationRadiation that is always present in the environment. Significant sources: radon gas in the air, rocks and buildings, food and drink, and cosmic rays.
Corrected count rate = measured count rate − background count rate. Always subtract background before doing half-life work.

5.2.2 The three emissions. Emission from a nucleus is spontaneous and random in direction.

Alpha (α)Beta (β⁻)Gamma (γ)
What it is2 protons + 2 neutrons (a helium nucleus)A high-speed electron from the nucleusHigh-frequency electromagnetic wave
Charge+2−10
Ionising effectStrongestModerateWeakest
Penetrating powerWeakest — stopped by paper/skinModerate — stopped by a few mm of aluminiumStrongest — reduced by thick lead or concrete
Deflection in fieldsDeflected (opposite to β), small deflectionDeflected (opposite to α), large deflectionNot deflected (no charge)
Notice that ionising power and penetrating power are opposites. Alpha ionises strongly precisely because it interacts so much — which is also why it loses energy quickly and cannot penetrate far.

5.2.3 Decay equations.

Method — balancing decay equations
  • Alpha decay: A decreases by 4, Z decreases by 2.
  • Beta decay: A is unchanged, Z increases by 1 (a neutron becomes a proton plus the emitted electron).
  • Gamma emission: neither A nor Z changes — only energy is lost.
  • Check that the top numbers balance and the bottom numbers balance on each side.
Worked example

Write the decay equations for (a) uranium-238 emitting an alpha particle, (b) carbon-14 emitting a beta particle.

  1. (a) 23892U → 23490Th + 42He  (238 = 234 + 4 ✓, 92 = 90 + 2 ✓)
  2. (b) 146C → 147N + 0−1e  (14 = 14 + 0 ✓, 6 = 7 + (−1) ✓)

5.2.4 Fission and fusion. Fusion is the formation of a larger nucleus by combining two smaller nuclei, releasing energy — this powers the stars. Fission is when a large nucleus such as U-235 absorbs a neutron and splits into daughter nuclei plus two or more neutrons, releasing energy. Those neutrons can cause further fissions — a chain reaction. In a reactor this is controlled by control rods (absorb neutrons to control the rate), a moderator (slows neutrons so they cause further fission) and a coolant (carries energy away to generate steam).

5.2.5 Half-life.

DefinitionThe half-life of an isotope is the time taken for half the nuclei of that isotope in any sample to decay.
Worked example

A source has a corrected count rate of 800 counts/minute. Its half-life is 6.0 hours. Find the corrected count rate after 24 hours.

  1. Number of half-lives = 24 ÷ 6.0 = 4
  2. Halve four times: 800 → 400 → 200 → 100 → 50 counts/minute

Carbon dating: living things absorb carbon-14; when they die, absorption stops and the C-14 decays with a known half-life, so the remaining proportion gives the age.

ApplicationRadiation and half-life neededWhy
Household smoke alarmAlpha, long half-lifeAlpha ionises air to complete a circuit but is stopped by smoke; long half-life avoids frequent replacement
Irradiating food / sterilising equipmentGammaPenetrates packaging to kill bacteria without opening it
Measuring/controlling material thicknessBetaPartly absorbed by the sheet, so the count rate detects thickness changes (alpha would be stopped entirely, gamma would pass through unaffected)
Diagnosis and treatment of cancerGammaPenetrates to reach tumours inside the body

5.2.6 Safety. Ionising radiation causes cell death, mutations and cancer in living things. Reduce risk by: reducing exposure time, increasing distance between source and body, and using shielding (lead, thick concrete) to absorb the radiation. Handle sources with tongs, point them away from people, and store them in lead-lined containers.

Skill check: A sample's count rate falls from 640 to 40 counts/s in 12 hours (background already subtracted). Find the half-life.
Solution: 640 → 320 → 160 → 80 → 40 is 4 half-lives. Half-life = 12 ÷ 4 = 3.0 hours.
Topic 6 · 2 units

Space physics

Mostly recall, with one equation and one long "describe the life cycle of a star" answer that appears regularly. Learn the star sequence as two branches — less massive and more massive — and it becomes easy marks.

6.1Earth and the Solar System

  • The Earth orbits the Sun once in approximately 365 days, along an ellipse that is approximately circular.
  • The Earth rotates once on its tilted axis in approximately 24 hours (this gives day and night; the tilt gives the seasons).
  • The Moon takes approximately one month to orbit the Earth.
  • Light from the Sun takes approximately 500 s to reach the Earth.
v = 2πr / T  (average orbital speed; r = average orbital radius, T = orbital period)
Worked example

The Earth's orbital radius is 1.5 × 10¹¹ m and its orbital period is 3.15 × 10⁷ s. Find its average orbital speed.

  1. v = 2πr/T = (2 × π × 1.5 × 10¹¹) ÷ (3.15 × 10⁷)
  2. = (9.42 × 10¹¹) ÷ (3.15 × 10⁷) = 3.0 × 10⁴ m/s (about 30 km/s)

The Solar System contains one star (the Sun), eight planets — in order from the Sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune — plus minor planets (dwarf planets such as Pluto, and asteroids in the asteroid belt), moons orbiting planets, and smaller bodies including comets and natural satellites.

  • The force keeping objects in orbit around the Sun is the Sun's gravitational attraction.
  • Gravitational field strength at a planet's surface depends on the planet's mass, and decreases with distance from the planet.
  • The Sun contains most of the mass of the Solar System, so its surface gravitational field strength is greater than any planet's.
  • The Sun's gravitational field strength decreases with distance, and so orbital speeds of the planets decrease the further they are from the Sun (and their orbital periods increase).
Skill check: Neptune is much further from the Sun than Earth. State and explain how its orbital speed compares with Earth's.
Solution: Neptune's orbital speed is smaller. The Sun's gravitational field strength decreases with distance, so the force providing Neptune's orbital motion is much weaker, and planets further from the Sun travel more slowly (and take far longer to complete an orbit).

6.2Stars and the Universe

6.2.1 The Sun as a star. The Sun is a medium-sized star made mostly of hydrogen and helium, radiating most of its energy in the infrared, visible and ultraviolet regions. Stars are powered by nuclear reactions; in stable stars this is the fusion of hydrogen into helium.

6.2.2 Stars and galaxies. Galaxies each contain many billions of stars. The Sun is a star in the Milky Way, whose diameter is about 100 000 light-years. Other Milky Way stars are much further from Earth than the Sun is. A light-year is the distance travelled in a vacuum by light in one year.

The life cycle of a star — learn both branches
  1. A star forms from an interstellar cloud of gas and dust containing hydrogen.
  2. The cloud collapses under its own gravitational attraction and heats up, becoming a protostar.
  3. It becomes a stable star when the inward force of gravitational attraction is balanced by an outward force due to the high temperature in its centre.
  4. Eventually the hydrogen fuel runs out.
  5. Less massive star: expands to a red giant → forms a planetary nebula with a white dwarf at its centre.
  6. More massive star: expands to a red supergiant → explodes as a supernova → leaves a neutron star or a black hole, and forms a nebula containing hydrogen and new heavier elements.
  7. That nebula may form new stars with orbiting planets.

6.2.3 The Universe. The Milky Way is one of many billions of galaxies making up the Universe.

Redshift and the Big BangRedshift is an increase in the observed wavelength of electromagnetic radiation emitted from receding stars and galaxies.
Light from distant galaxies shows redshift, and the further away the galaxy, the greater the redshift — so the faster it is moving away from Earth. This means the Universe is expanding in all directions, which suggests it began from a single point: evidence for the Big Bang theory.
Skill check: Explain why a more massive star has a different fate from a less massive one.
Solution: A more massive star has a much stronger inward gravitational attraction, so when fusion can no longer support it the collapse is far more violent. It expands to a red supergiant and explodes as a supernova, leaving a neutron star or black hole — whereas a less massive star ends quietly as a red giant shedding a planetary nebula and leaving a white dwarf.
Worth 20% of your grade

Practical skills — Paper 3 and Paper 4

Everyone sits one practical paper, and it is pure AO3. Whether you take the real Practical Test (P3) or the Alternative to Practical (P4), the examined skills are identical — the only difference is whether you hold the apparatus. This section is the part of the syllabus most students never revise, and it is a fifth of the marks.

The experimental contexts you must be familiar with

  • Measuring physical quantities such as length, volume or force
  • Measuring small distances or short time intervals
  • Determining a derived quantity — extension per unit load for a spring, a resistance value, an acceleration
  • Testing a relationship between two variables, e.g. p.d. across a wire against its length
  • Comparing measured quantities (such as angles of reflection) or derived quantities (such as density)
  • Cooling and heating, including temperature measurement
  • Experiments using springs and balances; timing motion or oscillations
  • Electric circuits — connecting and reconnecting circuits, measuring current and p.d.
  • Optics — optical pins, mirrors, prisms, lenses, glass or Perspex blocks (rectangular and semicircular)
  • Unfamiliar procedures with simple apparatus (they will describe what to do — read carefully)

Planning: the language that earns marks

Variables — name them explicitly
  • Independent variable: the one you deliberately change.
  • Dependent variable: the one you measure.
  • Control variables: the ones you keep constant — and you must say why: "so that any change in the dependent variable is caused only by the independent variable."

A good plan states: the apparatus, how to measure each quantity, a sensible range and number of values (usually at least 5–6 spread across a wide range), what to keep constant, how results will be recorded, how they will be processed (often a graph), and the safety precautions.

When asked to justify a choice of apparatus, refer to precision and range: "a micrometer, because it reads to 0.01 mm which is precise enough for a wire's diameter" beats "a micrometer because it is accurate".

Taking readings

  • Read to the nearest half-scale division where required (e.g. a ruler marked in mm can be read to 0.5 mm).
  • Correct for zero errors — if a force meter reads 0.2 N with nothing attached, subtract 0.2 N from every reading.
  • Avoid parallax error: read at eye level, perpendicular to the scale; use a mirror behind the pointer if provided.
  • Repeat readings and average them, especially for timings.
  • Time multiple oscillations (e.g. 20) and divide, to reduce the percentage uncertainty from reaction time.
  • Record all readings to the same number of decimal places, consistent with the instrument's precision.
Tables — the rules examiners apply
  • Every column heading has a quantity and a unit, separated properly: length / cm, time / s, 1/R / Ω⁻¹.
  • Units go in the heading only, never beside each number.
  • Raw readings in a column all have the same number of decimal places.
  • Calculated values are given to a sensible number of significant figures — no more than the raw data justifies.

Graphs — where marks are most often lost

Checklist for every graph you draw
  1. Axes labelled with quantity and unit, independent variable on the x-axis.
  2. Sensible scale — the plotted points should fill at least half the grid in both directions. Never use awkward scales like 3 units per square.
  3. Plot accurately with small neat crosses (×) or dots in circles, to within half a small square.
  4. Best-fit line: a single thin ruled straight line (or a smooth curve) with points balanced either side. Do not join the dots.
  5. Gradient: draw a large triangle using points on the line (not data points), spanning at least half the line, and show the substitution: gradient = Δy ÷ Δx, with units.
  6. Intercept: read only where the axis is at zero; otherwise substitute a point from the line into y = mx + c.
length / cm resistance / Ω Δx Δy
A large gradient triangle drawn on the best-fit line — not between two data points — spanning most of the line.

Evaluating: errors, improvements and conclusions

Type of errorWhat it doesHow to reduce it
Random (reaction time, judging a reading)Scatters results either side of the true valueRepeat and average; time multiple oscillations; use a larger measurement
Systematic (zero error, wrongly calibrated scale)Shifts every result the same wayCheck and correct the zero; a graph intercept can reveal it
ParallaxConsistent misreading of a scaleView perpendicular to the scale, at eye level
Heat loss (thermal experiments)Makes measured energy or heat capacity too highInsulate; use a lid; start below and end above room temperature
Answering "suggest an improvement"Never write "be more careful" or "use better equipment". Name a specific change and say what it fixes: "insulate the block with foam to reduce energy transfer to the surroundings", "use a set square so the ruler is vertical", "take readings at 10 cm intervals over a wider range", "repeat each timing three times and take a mean".
Answering "is the conclusion supported?"Quote actual numbers from the results, then judge. "The student says R is proportional to L. Doubling L from 20 cm to 40 cm changes R from 2.1 Ω to 4.3 Ω, which is approximately double, so the results do support the conclusion within experimental error." Naming the comparison is what scores.

Safety precautions should match the hazard: hot apparatus → use tongs/heatproof mat and allow to cool; masses on a spring → keep feet clear and use a soft landing; electrical work → switch off between changes and avoid overheating the wire; light sources and lasers → never look directly at the beam.

Reference

Definitions bank

Physics definitions are marked strictly — the wording carries the mark. These are the ones asked most often, phrased the way examiners expect.

TermDefinition
Scalar / vectorA scalar has magnitude only; a vector has magnitude and direction
SpeedDistance travelled per unit time
VelocityChange in displacement per unit time
AccelerationChange in velocity per unit time
MassA measure of the quantity of matter in an object; it resists change from its state of rest or motion
WeightThe gravitational force acting on an object
Gravitational field strengthForce per unit mass (equal to the acceleration of free fall)
DensityMass per unit volume
Newton's first lawAn object either remains at rest or continues to move in a straight line at constant speed unless acted on by a resultant force
Newton's third lawWhen object A exerts a force on object B, object B exerts an equal and opposite force on object A
Spring constantForce per unit extension
Limit of proportionalityThe point beyond which extension is no longer proportional to load
Moment of a forceForce × perpendicular distance from the pivot
Principle of momentsFor an object in equilibrium, the sum of the clockwise moments about a pivot equals the sum of the anticlockwise moments
Centre of gravityThe point at which the whole weight of an object may be considered to act
MomentumMass × velocity
ImpulseForce × the time for which the force acts
Conservation of momentumTotal momentum before = total momentum after, when no external force acts
Conservation of energyEnergy cannot be created or destroyed, only transferred between stores; the total is constant
Work doneForce × distance moved in the direction of the force
PowerWork done per unit time, or energy transferred per unit time
EfficiencyUseful energy (or power) output ÷ total input, often × 100%
PressureForce per unit area
Specific heat capacityThe energy required per unit mass per unit temperature increase
Latent heatThe energy required to change the state of a substance (without a change in temperature)
EvaporationThe escape of the more energetic particles from the surface of a liquid
FrequencyThe number of wavelengths that pass a point per unit time
WavelengthThe distance between two consecutive identical points, e.g. two consecutive crests
AmplitudeThe maximum distance from the mean position
Transverse waveVibration at right angles to the direction of energy transfer
Longitudinal waveVibration parallel to the direction of energy transfer
Refractive indexn = sin i ÷ sin r
Critical angleThe angle of incidence in the denser medium for which the angle of refraction is 90°
Total internal reflectionAll light is reflected back into the denser medium when the angle of incidence exceeds the critical angle
Real / virtual imageA real image is formed by converging rays (can be projected); a virtual image is formed by diverging rays (cannot)
UltrasoundSound with a frequency higher than 20 kHz
Magnetic fieldA region in which a magnetic pole experiences a force
Electric fieldA region in which an electric charge experiences a force
Electric currentThe charge passing a point per unit time
e.m.f.The electrical work done by a source in moving a unit charge around a complete circuit
Potential differenceThe work done by a unit charge passing through a component
Ohm's lawCurrent is directly proportional to p.d., provided the temperature is constant
Lenz's lawThe effect of the current produced by an induced e.m.f. is to oppose the change producing it
Proton number ZThe number of protons in a nucleus
Nucleon number AThe total number of protons and neutrons in a nucleus
IsotopesAtoms of the same element with the same proton number but different numbers of neutrons
Half-lifeThe time taken for half the nuclei of that isotope in any sample to decay
Background radiationRadiation that is always present in the environment, from sources such as radon gas, rocks, food and cosmic rays
Light-yearThe distance travelled in a vacuum by light in one year
RedshiftAn increase in the observed wavelength of electromagnetic radiation emitted from receding stars and galaxies
Reference

Free past papers & how to revise physics

Official (free)

  • Cambridge International — 5054 subject page: syllabus, specimen papers, past papers, mark schemes and examiner reports.
  • Examiner reports say exactly which definitions and explanations candidates got wrong each series — read them for every paper you attempt.

Free archives

A method that fits how physics is marked

  1. Definitions first. Write the definitions bank on cards and test yourself until the wording is automatic — that is pure AO1, half the paper.
  2. Equations second. Write out the full equation list from blank paper once a week. Nothing is given to you in the exam.
  3. Then calculations. Always: write the equation, substitute with units, then evaluate. Method marks survive an arithmetic slip; a bare wrong answer scores nothing.
  4. Explanations third. Practise the standard "explain in terms of particles/forces/energy" answers out loud until they are structured, not vague.
  5. Do not skip the practical paper. Work through past P3/P4 papers specifically — 20% of your grade, and the questions repeat their patterns heavily.

Edvia Free Resources — O Level Physics 5054. Original notes and worked examples written for the Cambridge O Level Physics 5054 syllabus for examination in 2026, 2027 and 2028. An independent free study resource, not affiliated with or endorsed by Cambridge University Press & Assessment. Syllabus reference codes are used for navigation. Share it freely — it will always be free.

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