Cambridge IGCSE / A‑Level Physics (9702) – Comprehensive Revision Notes
Assessment Objectives (AO)
- AO1 – Knowledge & Understanding: recall definitions, formulas and concepts.
- AO2 – Application: use knowledge to solve quantitative problems and interpret diagrams.
- AO3 – Practical & Experimental Skills: plan investigations, analyse data, evaluate uncertainties (Paper 3/5).
Common Symbols & Units
| Symbol | Quantity | Unit | Typical Formula |
|---|
| x | Displacement from equilibrium | m | ‑ |
| x_0 | Amplitude | m | ‑ |
| t | Time | s | ‑ |
| v | Velocity | m s⁻¹ | v = dx/dt |
| a | Acceleration | m s⁻² | a = dv/dt = d²x/dt² |
| ω | Angular frequency | rad s⁻¹ | ω = √(k/m) = √(g/L) … |
| f | Frequency | Hz | f = ω/2π |
| T | Period | s | T = 1/f = 2π/ω |
| φ | Phase constant | rad | ‑ |
| k | Spring constant | N m⁻¹ | ‑ |
| m | Mass | kg | ‑ |
| g | Acceleration due to gravity | m s⁻² | ≈9.81 |
| I | Moment of inertia | kg m² | ‑ |
| Q | Electric charge | C | ‑ |
| V | Potential difference | V | ‑ |
| R | Resistance | Ω | ‑ |
| C | Capacitance | F | ‑ |
| μ₀, ε₀ | Permeability & permittivity of free space | H m⁻¹, F m⁻¹ | ‑ |
1. AS‑Level Topics (1‑11)
1.1 Quantities, Units & Prefixes
- SI base units and derived units.
- Common prefixes (k, M, m, µ, n) and conversion practice.
1.2 Kinematics (Straight‑line Motion)
| Equation | When to use |
|---|
| v = u + at | constant acceleration |
| s = ut + ½at² | displacement with known u, a |
| v² = u² + 2as | no time needed |
Example: A car accelerates from rest at 2 m s⁻² for 5 s. Find its final speed and distance travelled.
- v = 0 + (2)(5) = 10 m s⁻¹
- s = 0·5 + ½(2)(5)² = 25 m
1.3 Forces & Dynamics
- Newton’s 1st, 2nd, 3rd laws.
- Weight, normal reaction, tension, friction (μs, μk).
- Resultant force: ΣF = ma.
Example: A 3 kg block slides down a 30° incline with μk = 0.15. Find acceleration.
Component of weight down the plane: mg sin 30° = 3·9.81·0.5 = 14.7 N.
Friction: μk N = 0.15·mg cos 30° = 0.15·3·9.81·0.866 ≈ 3.8 N.
Net force = 14.7 – 3.8 = 10.9 N ⇒ a = F/m = 10.9/3 ≈ 3.6 m s⁻².
1.4 Energy, Work & Power
| Quantity | Formula | Units |
|---|
| Work | W = F·s·cosθ | J |
| Kinetic energy | K = ½mv² | J |
| Gravitational potential energy | U = mgh | J |
| Power | P = W/t = Fv | W |
Example: A 0.5 kg ball is dropped from 2 m. Find speed just before impact (ignore air resistance).
mgh = ½mv² ⇒ v = √(2gh) = √(2·9.81·2) ≈ 6.26 m s⁻¹.
1.5 Momentum & Collisions
- Linear momentum p = mv.
- Impulse J = Δp = FΔt.
- Conservation of momentum for isolated systems (elastic & inelastic).
Example (elastic): 0.2 kg bullet (v = 400 m s⁻¹) embeds in 0.8 kg block initially at rest. Find final speed.
p_initial = 0.2·400 = 80 kg m s⁻¹.
p_final = (0.2+0.8)v ⇒ v = 80/1.0 = 80 m s⁻¹.
1.6 Material Properties & Deformation
| Quantity | Formula | Units |
|---|
| Stress | σ = F/A | Pa |
| Strain | ε = ΔL/L | ‑ (dimensionless) |
| Young’s modulus | E = σ/ε | Pa |
| Hooke’s law | F = –k x | N |
Example: A steel wire (A = 2 mm², E = 2×10¹¹ Pa) is stretched by 1 mm. Find the force.
ΔL/L = 0.001/0.5 m = 2×10⁻³ (assuming original length 0.5 m).
σ = E·ε = 2×10¹¹·2×10⁻³ = 4×10⁸ Pa.
F = σA = 4×10⁸·2×10⁻⁶ = 800 N.
1.7 Waves
- Wave speed v = fλ.
- Longitudinal vs transverse.
- Superposition & standing waves.
Example: A string fixed at both ends vibrates at its fundamental frequency of 120 Hz with wavelength 2 m. Find wave speed.
v = fλ = 120·2 = 240 m s⁻¹.
1.8 Electricity (Static)
| Quantity | Formula |
|---|
| Charge | Q = It |
| Current density | J = σE |
| Coulomb’s law | F = k_e Q₁Q₂/r² |
Example: A current of 3 A flows for 5 s. Find charge transferred.
Q = It = 3·5 = 15 C.
1.9 D.C. Circuits
- Ohm’s law: V = IR.
- Series: R_eq = ΣR, V_total = ΣV, I same.
- Parallel: 1/R_eq = Σ1/R, I_total = ΣI, V same.
- Kirchhoff’s rules (junction & loop).
Example (parallel): Two resistors, 4 Ω and 6 Ω, are connected across a 12 V battery. Find total current.
1/R_eq = 1/4 + 1/6 = (3+2)/12 = 5/12 ⇒ R_eq = 12/5 = 2.4 Ω.
I = V/R_eq = 12/2.4 = 5 A.
1.10 Particle Physics
- Charge, mass, and spin of common particles (e, p, n, α, β).
- Radioactive decay types: α, β⁻, β⁺, γ.
- Half‑life law: N = N₀e^{-λt}, λ = ln2 / t_{½}.
Example: A sample contains 1.0 g of ^{60}Co (t_{½}=5.27 yr). How many atoms remain after 10 yr?
Number initially N₀ = (1.0 g / 60 g mol⁻¹)·6.02×10²³ ≈ 1.00×10²².
λ = ln2 / 5.27 yr = 0.131 yr⁻¹.
N = N₀ e^{-λ·10} ≈ 1.00×10²²·e^{-1.31} ≈ 2.7×10²¹ atoms.
1.11 Simple Harmonic Motion (SHM)
Fundamental Equation
$$\frac{d^{2}x}{dt^{2}} = -\omega^{2}x \qquad\text{(acceleration opposite to displacement)}
General Solution
$$x(t)=x_{0}\sin(\omega t+\phi)$$
- Amplitude x₀ – maximum displacement.
- Angular frequency ω – determines period T = 2π/ω.
- Phase constant φ – set by initial conditions.
Deriving ω for Common Systems
- Mass‑spring system (Hooke’s law, F = –kx):
- ma = –kx ⇒ a = –(k/m)x.
- Compare with a = –ω²x ⇒ ω = √(k/m).
- Simple pendulum (small‑angle):
- Torque τ = –mgL sinθ ≈ –mgLθ.
- Iα = τ with I = mL² ⇒ mL² θ̈ = –mgLθ.
- θ̈ = –(g/L)θ ⇒ ω = √(g/L).
Velocity & Acceleration
$$v(t)=\frac{dx}{dt}= \omega x_{0}\cos(\omega t+\phi)$$
$$a(t)=\frac{d^{2}x}{dt^{2}}= -\omega^{2}x_{0}\sin(\omega t+\phi)= -\omega^{2}x(t)$$
Energy in SHM
| Quantity | Expression |
|---|
| Maximum kinetic energy | K_{max}=½mω²x₀² |
| Maximum potential (elastic) energy | U_{max}=½k x₀² = ½mω²x₀² |
| Total mechanical energy | E = K + U = ½k x₀² (constant) |
Worked Example (Mass‑spring)
Problem: A 0.5 kg mass attached to a spring (k = 200 N m⁻¹) is pulled 0.10 m from equilibrium and released from rest. Find its displacement after 0.05 s.
- ω = √(k/m) = √(200/0.5) = 20 rad s⁻¹.
- Initial conditions: x(0)=0.10 m, v(0)=0 ⇒ φ = –π/2, so use cosine form:
$$x(t)=x_{0}\cos(\omega t)$$
- x(0.05)=0.10 cos(20·0.05)=0.10 cos 1.0 ≈ 0.054 m.
2. A‑Level Extensions (Topics 12‑25)
2.1 Circular Motion
- Uniform circular motion: a_c = v²/r = ω²r.
- Period T = 2πr/v = 2π/ω.
Example: A car rounds a curve of radius 50 m at 20 m s⁻¹. Find centripetal acceleration.
a_c = v²/r = 20²/50 = 8 m s⁻².
2.2 Gravitation
| Quantity | Formula |
|---|
| Gravitational force | F = G M m / r² |
| Field strength | g = GM / r² |
| Orbital speed (circular) | v = √(GM/r) |
| Period of satellite | T = 2π√(r³/GM) |
2.3 Thermodynamics – Ideal Gas & First Law
- Ideal‑gas equation: pV = nRT.
- First law: ΔU = Q – W.
- For a monatomic ideal gas: U = (3/2)nRT.
Example: 1 mol of an ideal gas is heated from 300 K to 400 K at constant volume. Find ΔU.
ΔU = (3/2)nRΔT = 1.5·8.31·(400–300) ≈ 1245 J.
2.4 Kinetic Theory of Gases
- Mean kinetic energy: ½ m ⟨v²⟩ = (3/2)k_B T.
- Pressure from molecular impacts: p = (1/3) N m ⟨v²⟩/V.
2.5 Damped, Forced & Resonant Oscillations
Equation of motion (damped):
$$m\ddot{x}+b\dot{x}+kx=0$$
Natural frequency ω₀ = √(k/m); damping ratio ζ = b/(2√{mk}).
Resonance occurs when driving frequency ω ≈ ω₀ (small ζ).
2.6 Electric & Magnetic Fields
| Quantity | Formula |
|---|
| Electric field | E = F/q = V/d (for uniform field) |
| Magnetic field (Biot‑Savart) | B = μ₀I/2πr (long straight wire) |
| Force on moving charge | F = q(v×B) |
2.7 A.C. Circuits
- rms values: V_{rms}=V_{max}/√2, I_{rms}=I_{max}/√2.
- Impedance: Z = √(R²+(X_L−X_C)²).
- Resonance in series LCR: ω₀ = 1/√(LC).
2.8 Quantum Physics
- Photoelectric equation: hf = Φ + ½mv_{max}².
- De Broglie wavelength: λ = h/p.
- Energy levels of hydrogen: E_n = –13.6 eV / n².
2.9 Nuclear Physics
- Binding energy per nucleon, mass–energy equivalence (E=Δmc²).
- Fission: heavy nucleus → lighter fragments + neutrons + energy.
- Fusion: light nuclei combine, releasing energy.
2.10 Medical Physics (Imaging)
- X‑ray production: bremsstrahlung & characteristic radiation.
- Attenuation: I = I₀e^{-μx} (μ = linear attenuation coefficient).
- CT number (Hounsfield unit): HU = 1000·(μ−μ_{water})/μ_{water}.
2.11 Astronomy
- Hubble’s law: v = H₀d.
- Luminosity distance, apparent & absolute magnitude relation.
- Kepler’s laws (derived from gravitation).
3. Practical & Experimental Toolbox (AO3)
3.1 Planning an Investigation
- State a clear, testable hypothesis.
- Identify independent, dependent and controlled variables.
- Choose appropriate apparatus (ensure safety & calibration).
- Sketch a labelled diagram of the set‑up.
- Write a step‑by‑step method (include repeatability).
3.2 Data Collection & Presentation
- Record raw data in a table with units and uncertainties.
- Use digital timers, multimeters, or Vernier sensors where possible.
- Plot graphs with correctly labelled axes, error bars, and best‑fit lines.
3.3 Uncertainty Analysis
- Identify sources of random error (reading, timing) and systematic error (zero‑offset, friction).
- Calculate absolute and relative uncertainties (Δx, Δx/x).
- Propagate uncertainties using:
- Addition/subtraction: Δz = √(Δa²+Δb²).
- Multiplication/division: (Δz/z) = √((Δa/a)²+(Δb/b)²).
- State final result to the appropriate number of significant figures.
3.4 Sample Investigation – Period of a Simple Pendulum
| Step | Action |
|---|
| 1 | Set up a light string of length L = 0.50 m with a small bob; attach a stopwatch. |
| 2 | Displace the bob by ≤ 5° and release; measure the time for 20 complete oscillations. Repeat three times. |
| 3 | Average the three total times, then divide by 20 to obtain T. |
| 4 | Calculate g using g = 4π²L/T² and propagate uncertainties from L (±0.001 m) and T (stopwatch ±0.2 s). |
Typical result: T ≈ 1.42 s → g ≈ 9.8 m s⁻² (within experimental uncertainty).
3.5 Mark‑scheme Tips for Paper 3/5
- Show a clear hypothesis, method, and risk assessment (5 marks).
- Present data in a well‑labelled table and graph (5 marks).
- Include a quantitative analysis with uncertainties (5 marks).
- Discuss limitations, improvements and evaluate the conclusion (5 marks).
4. Quick Revision Checklist (Cambridge 9702)
- Can you write the differential equation
¨x = –ω²x and explain its physical meaning?
- Do you know how to obtain
ω for a mass‑spring system and for a simple pendulum?
- Can you express the general SHM solution
x(t)=x₀ sin(ωt+φ) and determine φ from any pair of initial conditions?
- Are you able to convert between
f, ω, T and use the correct units?
- Can you calculate kinetic, potential and total energy in SHM and show energy conservation?
- Do you understand the derivations and key formulas for all AS‑level topics (1‑11) and A‑level extensions (12‑25)?
- Are you comfortable planning a practical, analysing uncertainties and presenting data as required for AO3?
- Can you apply
a = –ω²x directly to find displacement, velocity or acceleration at a given time?
5. Suggested Diagram (Insert when printing)
Mass‑spring system: a block of mass m attached to a horizontal spring (constant k) displaced a distance x from equilibrium. Arrows indicate the restoring force F = –kx and the resulting acceleration a = –ω²x toward the equilibrium position.