1 Motion, Forces & Energy
1.1 Speed, velocity and acceleration
Speed – scalar, \(v = \dfrac{s}{t}\) (m s⁻¹).
Velocity – vector, magnitude = speed, direction given by the line of motion.
Acceleration – change of velocity per unit time, \(a = \dfrac{\Delta v}{\Delta t}\) (m s⁻²).
Typical exam question: a car increases its speed from 10 m s⁻¹ to 30 m s⁻¹ in 5 s – calculate its acceleration.
1.2 Distance‑time and velocity‑time graphs
Gradient of a distance‑time graph = speed.
Gradient of a velocity‑time graph = acceleration.
Area under a velocity‑time graph = displacement.
Students should be able to sketch, interpret and calculate values from the three basic graph types.
1.3 Forces and motion
Resultant (net) force, \(\sum\mathbf{F}=m\mathbf{a}\) (Newton’s 2nd law).
Weight \(W=mg\) (downward), normal reaction, tension, friction (static & kinetic).
Moments: \(\tau = Fr\) – clockwise vs anti‑clockwise.
Practical: using a spring balance and a friction‑less air track to verify \(F=ma\).
1.4 Momentum and impulse
Momentum \(p = mv\).
Impulse \(J = F\Delta t = \Delta p\).
Conservation of momentum in collisions (elastic & inelastic).
1.5 Work, energy, power
Work \(W = F s \cos\theta\) (J). Positive when force has a component in the direction of motion.
Kinetic energy \(Ek = \frac12 mv^2\). Gravitational potential energy \(E p = mgh\).
Conservation of energy – total energy before = total energy after (neglecting losses).
Power \(P = \dfrac{W}{t} = Fv = \dfrac{E}{t}\) (W).
1.6 Energy resources (1.7 in the syllabus)
1.6.1 Energy‑flow (Sankey) diagram
The diagram below shows the typical pathway from a primary energy source to the useful end‑use. It is the visual representation the syllabus expects students to be able to describe.
Primary source
Conversion
(e.g. turbine)
Electricity
End‑use
Fuel / Heat
Electrical power
Lighting, heating, transport …
1.6.2 Link to other syllabus sections
Section 2.3 (Heat transfer) – conversion of thermal energy from combustion.
Section 4.2 (Electrical energy and power) – generation of electricity in turbines and generators.
Section 4.5 (Power in electrical circuits) – distribution and use of generated electricity.
Section 5.2 (Nuclear physics) – fission process that powers nuclear reactors.
1.6.3 Efficiency – qualitative overview
Efficiency = (useful energy output ÷ total energy input) × 100 %.
Thermal plants (coal, oil, natural gas) – limited by the Carnot cycle; typical efficiencies: coal ≈ 30–35 %, oil ≈ 35–40 %, modern combined‑cycle gas ≈ 45–60 %.
Nuclear power – thermal efficiency ≈ 33 % but fuel energy density is ≈ 10⁸ times higher than coal.
Renewables – expressed as capacity factor (average output ÷ rated output):
Solar PV ≈ 15–20 %.
Wind ≈ 30–40 %.
Large‑scale hydro ≈ 50–90 % (steady flow).
Biomass – direct combustion ≈ 20 %; modern gasification up to ≈ 35 %.
1.6.4 Quantitative comparison of energy densities (per unit mass)
Energy source Typical energy density Typical efficiency (thermal or capacity factor)
Coal ≈ 24 MJ kg⁻¹ 30–35 %
Crude oil (gasoline) ≈ 42 MJ kg⁻¹ 35–40 %
Natural gas (methane) ≈ 55 MJ kg⁻¹ 45–60 % (combined‑cycle)
Uranium‑235 (fission) ≈ 8 × 10⁷ MJ kg⁻¹ ≈ 33 % (thermal)
Solar PV (silicon) ≈ 0.15 MJ kg⁻¹ (panel) → 15–20 % conversion 15–20 %
Wind (average) ≈ 0.5 MJ m⁻³ (air kinetic energy) 30–40 % (capacity factor)
Hydro (large dam) Variable – depends on head and flow 50–90 %
Geothermal (dry steam) ≈ 0.1 MJ kg⁻¹ of water steam ≈ 10–20 % (overall plant)
1.6.5 Energy sources – advantages, disadvantages & safety
Coal (solid fossil fuel)
Factor Assessment
Renewability Non‑renewable – formation takes millions of years.
Availability Large global reserves; uneven geographic distribution.
Reliability High – can be stock‑piled and used on demand.
Scale Very large – single plants can generate several gigawatts.
Environmental impact High CO₂, SO₂, NOₓ, particulate emissions; ash disposal; acid‑rain contribution.
Safety considerations Dust explosions in handling; miners at risk of pneumoconiosis (black‑lung).
Advantages
Established infrastructure; low fuel cost.
Stable, controllable output.
High energy density per unit volume.
Disadvantages
Major source of greenhouse‑gas emissions.
Air‑quality and health impacts.
Finite resource.
Oil (liquid fossil fuel)
Factor Assessment
Renewability Non‑renewable.
Availability Large reserves but geopolitically concentrated.
Reliability High – can be stored in tanks and transported worldwide.
Scale Large – powers transport, industry and a substantial share of electricity generation.
Environmental impact CO₂ emissions, oil spills, SOₓ, NOₓ, particulates.
Safety considerations Spill risk (marine & land), fire hazard, occupational exposure.
Advantages
Very high energy density (≈ 42 MJ kg⁻¹).
Versatile – fuels transport, heating, industry.
Extensive distribution network.
Disadvantages
Contributes to climate change.
Spill‑related habitat damage.
Finite supply.
Natural gas (primarily methane)
Factor Assessment
Renewability Non‑renewable.
Availability Abundant in many regions; transported via pipelines or LNG ships.
Reliability High – can be stored as compressed gas or liquefied.
Scale Large – major contributor to national grids.
Environmental impact Lower CO₂ per MJ than coal, but methane leakage (potent GHG) can offset benefits.
Safety considerations Flammable; explosion risk if leaks occur; requires strict pipeline monitoring.
Advantages
Cleaner combustion (less SO₂, NOₓ, particulates).
High efficiency in combined‑cycle plants (45–60 %).
Quick start‑up and shut‑down.
Disadvantages
Methane leakage contributes strongly to global warming.
Still a finite fossil resource.
Infrastructure cost for pipelines or LNG terminals.
Nuclear power (fission)
Factor Assessment
Renewability Non‑renewable (uranium finite) but fuel use is extremely low per unit energy.
Availability Uranium resources are globally distributed; breeder reactors could extend supply.
Reliability Very high – provides baseload power 24 h day⁻¹.
Scale Large – a single reactor can exceed 1 GW electrical output.
Environmental impact Low CO₂ during operation; issues include radioactive waste, mining impact and rare accidents.
Safety considerations Radiation protection, robust containment, emergency shutdown (SCRAM), waste management.
Advantages
Very low greenhouse‑gas emissions.
High power density – small land footprint.
Continuous, controllable output.
Disadvantages
Radioactive waste requires long‑term management.
High capital cost and long construction periods.
Public concern over safety and proliferation.
Solar photovoltaic (PV)
Factor Assessment
Renewability Renewable – sunlight is virtually inexhaustible on human timescales.
Availability Widely available; intensity varies with latitude, season and weather.
Reliability Intermittent – generation only when the sun shines; storage or backup needed.
Scale Modular – from small rooftop systems (~1 kW) to utility‑scale farms (> 500 MW).
Environmental impact Low operational emissions; manufacturing uses hazardous chemicals and electricity (often from the grid).
Safety considerations Electrical‑shock risk during installation; fire hazard if panels are damaged.
Advantages
No fuel cost; electricity is free after installation.
Scalable and can be sited close to demand.
Quiet, low‑maintenance, long lifespan (~25 years).
Disadvantages
Low capacity factor (≈ 15–20 %).
Large land area needed for utility farms.
Performance falls with high temperature.
Wind power
Factor Assessment
Renewability Renewable – wind is continuously replenished by solar heating of the atmosphere.
Availability Best in coastal, offshore and high‑latitude sites; varies with time.
Reliability Intermittent – output depends on wind speed; need grid integration or storage.
Scale Modular – from small 100 W turbines for homes to 3–5 MW offshore units.
Environmental impact Low emissions; visual impact, noise and possible bird/bat collisions.
Safety considerations Blade‑failure risk; safe siting away from populated areas.
Advantages
No fuel cost; low operating cost.
High capacity factor in windy regions (30–40 %).
Scalable and can be added incrementally.
Disadvantages
Intermittent; requires backup or storage.
Site‑specific – not suitable everywhere.
Infrastructure (roads, transmission) can be expensive.
Hydroelectric power (large dam)
Factor Assessment
Renewability Renewable – water cycle is driven by solar energy.
Availability Depends on geography (river flow, head). Good in mountainous regions.
Reliability Highly reliable; can provide baseload and rapid load‑following.
Scale Very large – megawatt to gigawatt plants.
Environmental impact Low emissions; but reservoir flooding can affect ecosystems and displace communities.
Safety considerations Dam failure risk; requires rigorous monitoring.
Advantages
High efficiency (50–90 %).
Long‑life, low operating cost.
Can store water for peak‑load generation.
Disadvantages
Geographically limited.
High initial capital and environmental/social impacts.
Susceptible to droughts.
Geothermal (dry‑steam & binary)
Factor Assessment
Renewability Renewable on human timescales where heat flow is sustained.
Availability Limited to tectonically active regions (e.g., Iceland, New Zealand, parts of USA).
Reliability High – provides baseload power, not weather dependent.
Scale Typically 10–100 MW per field; can be expanded.
Environmental impact Low emissions; possible release of trace gases, land subsidence.
Safety considerations High temperature fluids; need corrosion‑resistant materials.
Advantages
Stable, continuous output.
Small land footprint.
Low operating cost after development.
Disadvantages
Geographically restricted.
High upfront drilling costs.
Potential for induced seismicity.
Biomass (solid, liquid or gas)
Factor Assessment
Renewability Renewable if biomass is replanted or waste is used.
Availability Abundant in agricultural regions; depends on land use.
Reliability Can be stored and dispatched like fossil fuels.
Scale From small domestic stoves to 100 MW power stations.
Environmental impact CO₂ released, but considered part of short‑term carbon cycle; air‑quality concerns if combustion is incomplete.
Safety considerations Dust explosion risk; handling of bio‑fuels.
Advantages
Utilises waste materials.
Can provide baseload power.
Reduces dependence on imported fossil fuels.
Disadvantages
Lower energy density than fossil fuels.
Land competition with food production.
Potential deforestation if not managed sustainably.
2 Thermal Physics
2.1 Particle model & states of matter
Solids – particles vibrate about fixed positions; high density.
Liquids – particles close together but can move past each other; definite volume, no fixed shape.
Gases – particles far apart; fill container, pressure arises from collisions.
2.2 Temperature, heat and specific heat capacity
Temperature scales: Celsius (°C), Kelvin (K) – \(T(K)=t(°C)+273\).
Heat energy: \(Q = mc\Delta T\) (J), where \(c\) is specific heat capacity.
Latent heat: \(Q = mL\) for phase change (fusion, vaporisation).
Practical: heating equal masses of aluminium and copper and measuring temperature rise to determine \(c\).
2.3 Heat transfer
Conduction – transfer through solids; rate \( \dot Q = \dfrac{kA\Delta T}{d}\).
Convection – transfer by fluid motion; natural vs forced.
Radiation – electromagnetic waves; Stefan‑Boltzmann law \(P = \varepsilon\sigma A T^{4}\).
Experiment ideas: metal‑rod conduction test, heated water convection cell, infrared camera to view radiative heat loss.
3 Waves
3.1 Wave properties
Wave speed: \(v = f\lambda\) (m s⁻¹).
Frequency \(f\) (Hz) – number of cycles per second.
Wavelength \(\lambda\) – distance between successive crests.
Amplitude – maximum displacement from equilibrium.
3.2 Reflection, refraction & diffraction
Law of reflection: angle of incidence = angle of reflection.
Refraction: \( \dfrac{\sin i}{\sin r} = \dfrac{v1}{v 2}\) (Snell’s law).
Diffraction – bending around obstacles; more pronounced when obstacle size ≈ wavelength.
Practical: ripple tank to observe all three phenomena with a point source and a slit.
3.3 Sound
Longitudinal wave; speed in air ≈ 340 m s⁻¹ (temperature dependent).
Pitch ∝ frequency; loudness ∝ amplitude.
Resonance – standing waves in tubes (open‑closed, open‑open).
3.4 Light
Electromagnetic wave; visible spectrum 400–700 nm.
Behaviour similar to water waves: reflection, refraction, total internal reflection, diffraction.
Lens formula: \(\dfrac{1}{f} = \dfrac{1}{do} + \dfrac{1}{d i}\).
4 Electricity & Magnetism
4.1 Charge, electric field & potential difference
Charge \(q\) measured in coulombs (C); like charges repel, opposite attract.
Electric field \(E = \dfrac{F}{q}\) (N C⁻¹); direction of force on a positive test charge.
Potential difference \(V = \dfrac{W}{q}\) (V); work done moving charge between two points.
4.2 Current, resistance & Ohm’s law
Current \(I = \dfrac{q}{t}\) (A).
Resistance \(R = \dfrac{V}{I}\) (Ω); depends on material, length, cross‑section, temperature.
Power \(P = VI = I^{2}R = \dfrac{V^{2}}{R}\) (W).
Experiment: constructing series and parallel circuits with a bulb, ammeter and voltmeter to verify Ohm’s law.
4.3 Series and parallel circuits
Series – same current, voltages add; total resistance \(R{T}=R {1}+R_{2}+…\).
Parallel – same voltage, currents add; \(\dfrac{1}{R{T}} = \dfrac{1}{R {1}}+\dfrac{1}{R_{2}}+…\).
4.4 Domestic wiring & safety
Standard UK supply: 230 V AC, 50 Hz.
Protective devices: fuses, circuit breakers, RCDs.
Colour coding of conductors (brown live, blue neutral, green/yellow earth).
4.5 Magnetic fields
Field lines emerge from north pole, enter south pole.
Force on a moving charge: \(\mathbf{F}=q\mathbf{v}\times\mathbf{B}\).
Force on a current‑carrying conductor: \(F = BIL\sin\theta\).
4.6 Electromagnetic induction
Faraday’s law: induced emf \(\mathcal{E}= -\dfrac{d\Phi}{dt}\).
Lenz’s law – direction of induced current opposes change in flux.
Applications: AC generators, transformers, induction cookers.
Practical: moving a magnet through a coil and measuring the induced voltage with a galvanometer.
5 Radioactivity & Nuclear Physics
5.1 Types of radiation
Alpha (\(\alpha\)) – helium nucleus, +2 e, low penetration, stopped by paper.
Beta (\(\beta\)) – high‑speed electron (or positron), moderate penetration, stopped by aluminium foil.
Gamma (\(\gamma\)) – high‑energy photons, high penetration, requires lead or concrete shielding.
5.2 Radioactive decay & half‑life
Decay law: \(N = N_{0}e^{-\lambda t}\) where \(\lambda\) is decay constant.
Half‑life \(t_{1/2} = \dfrac{\ln2}{\lambda}\).
Applications: carbon dating, medical imaging (PET, gamma cameras), sterilisation.
5.3 Nuclear reactions
Fission – heavy nucleus splits, releasing neutrons, large energy release (≈ 200 MeV per fission).
Fusion – light nuclei combine (e.g., D + T → He + n), releases even more energy; requires extremely high temperature/pressure.
5.4 Safety & applications
Shielding, distance, time principle for protection.
Uses: electricity generation, cancer treatment (radiotherapy), food irradiation.
Issues: radioactive waste, proliferation, accidental release.