Know that the strength of the gravitational field (a) at the surface of a planet depends on the mass of the planet (b) around a planet decreases as the distance from the planet increases

IGCSE Physics 0625 – Complete Syllabus Notes (2026‑2028)

Learning Objectives (All Assessment Objectives)

• AO1 – Knowledge & Understanding: Define terms, state laws and formulae, and explain concepts across all syllabus areas.
• AO2 – Application: Use equations and principles to solve quantitative problems, predict outcomes and interpret data.
• AO3 – Practical Skills: Plan, carry out and evaluate investigations; analyse uncertainties; apply safety procedures.

Contents Overview

1. Motion, Forces & Energy
2. Thermal Physics
3. Waves
4. Electricity & Magnetism
5. Nuclear Physics
6. Space Physics
7. Practical Skills & Experiment Ideas
8. Summary Checklists & Quick Reference

1. Motion, Forces & Energy

Key Concepts & Formulae

• Scalars & Vectors: Scalars have magnitude only (e.g. speed, mass). Vectors have magnitude + direction (e.g. velocity, force). Use component method or right‑angle triangle for addition.
• Distance, Displacement, Speed, Velocity, Acceleration

  • v = s/t, a = Δv/Δt
  • Equations of motion (constant acceleration):

    • v = u + at
    • s = ut + ½at²
    • v² = u² + 2as

• Graphs: distance‑time, speed‑time, velocity‑time. Gradient = speed (or acceleration for v‑t); area under v‑t = displacement.
• Forces

  • Weight: W = mg
  • Normal reaction, tension, spring force F = kx (Hooke’s law, limit of proportionality)
  • Friction:

    • Static: F ≤ μₛN
    • Kinetic: F = μₖN
    • Fluid drag (approx. F = ½ CρAv² for high speeds)

  • Resultant force: vector sum of all forces (use components or right‑angle method).
  • Torque (moment of a force): τ = Fr sinθ. Rotational equilibrium when Στ = 0.
  • Centre of gravity: point where weight can be considered to act; for uniform objects it coincides with the geometric centre.

• Circular Motion

  • Centripetal force: F_c = mv²/r = mω²r
  • Required for any object moving in a circle; provided by tension, friction, gravity, etc.

• Momentum & Impulse

  • Momentum: p = mv
  • Impulse: I = FΔt = Δp
  • Conservation of momentum for isolated systems.

• Work, Energy & Power

  • Work: W = F·s cosθ (J)
  • Kinetic energy: E_k = ½mv²
  • Gravitational potential energy: E_p = mgh
  • Elastic potential energy (spring): E_s = ½kx²
  • Conservation of energy (isolated system).
  • Power: P = W/t = Fv = ΔE/Δt (W)
  • Efficiency: η = (useful energy output / total energy input) × 100 %

• Load‑Extension Graphs

  • Linear region obeys Hooke’s law; slope = spring constant k.
  • Beyond the limit of proportionality the graph curves, indicating permanent deformation.

Worked Example (Net Force)

A 2 kg cart accelerates from rest to 5 m s⁻¹ in 4 s. Find the net force.

1. Acceleration: a = Δv/Δt = 5/4 = 1.25 m s⁻²
2. Force: F = ma = 2 × 1.25 = 2.5 N

Worked Example (Torque)

A force of 30 N is applied at the end of a 0.5 m wrench making a 90° angle with the wrench. Calculate the torque.

τ = Fr sinθ = 30 × 0.5 × sin90° = 15 N·m

AO Mapping (Motion, Forces & Energy)

2. Thermal Physics

Fundamental Concepts

• Particle Model: Matter consists of particles in constant motion; temperature ↔ average kinetic energy.
• Specific Heat Capacity: Q = mcΔT
• Latent Heat: Q = mL (fusion = Lf, vaporisation = Lv)
• Thermal Expansion

  • Linear: ΔL = αL₀ΔT
  • Volumetric: ΔV = βV₀ΔT (β ≈ 3α for solids)

Heat Transfer – Quantitative Relationships

• Conduction (Fourier’s law):

  \[

  Q = \frac{kA}{L}\,(ΔT)

  \]

  where k = thermal conductivity (W m⁻¹ K⁻¹), A = cross‑sectional area, L = thickness.

• Convection (density‑driven flow):

  \[

  Q = hAΔT

  \]

  h = convection heat‑transfer coefficient (depends on fluid velocity, viscosity, surface roughness).

• Radiation (Stefan‑Boltzmann law):

  \[

  Q = εσAT^{4}

  \]

  ε = emissivity (0–1), σ = 5.67×10⁻⁸ W m⁻² K⁻⁴, T in kelvin.

Molecular‑Level Insight

• In metals, free electrons transfer kinetic energy rapidly → high k.
• In gases, energy is transferred by collisions; k is low, so conduction is weak.
• Radiation is emission of electromagnetic waves; all bodies emit, intensity ∝ T⁴.

Worked Example – Conduction

Calculate the heat flow through a 0.02 m thick copper plate (k = 400 W m⁻¹ K⁻¹) of area 0.5 m² when the temperature difference between its faces is 30 K.

\[

Q = \frac{kA}{L}ΔT = \frac{400×0.5}{0.02}×30 = 300\,000\ \text{W}

\]

Worked Example – Radiation

A blackbody sphere (ε = 1) has a surface temperature of 500 K and a radius of 0.1 m. Find the radiated power.

\[

A = 4πr^{2}=4π(0.1)^{2}=0.126 \text{m}^{2}

\]

\[

Q = εσAT^{4}=1×5.67×10^{-8}×0.126×(500)^{4}\approx 89 \text{W}

\]

Energy‑Balance Example – Earth’s Climate (Optional Extension)

Assume the Earth receives an average solar flux of 1360 W m⁻², but only a quarter is absorbed due to albedo. Using the Stefan‑Boltzmann law, estimate the equilibrium temperature (ignore atmosphere).

\[

\frac{1360}{4}=σT^{4}\;\Rightarrow\;T=(\frac{340}{5.67×10^{-8}})^{1/4}\approx 255 \text{K}

\]

AO Mapping (Thermal Physics)

3. Waves

Fundamental Properties

• Wave Types: Transverse (e.g., light) vs. longitudinal (e.g., sound).
• Speed–Frequency–Wavelength: v = fλ.
• Reflection & Refraction: Angle of incidence = angle of reflection; Snell’s law n₁sinθ₁ = n₂sinθ₂.
• Diffraction & Interference: Huygens’ principle; constructive when path difference = nλ, destructive when = (n + ½)λ.

Light

• Ray optics – mirrors (concave, convex) and lenses (converging, diverging).
• Lens formula: \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\).
• Dispersion → formation of a spectrum.
• Optical instruments (microscope, telescope) – magnification formulas.

Sound

• Production (vibrating source) → longitudinal wave.
• Speed depends on medium (air ≈ 340 m s⁻¹, water ≈ 1500 m s⁻¹, steel ≈ 5000 m s⁻¹).
• Pitch ↔ frequency; loudness ↔ amplitude/intensity.
• Ultrasound applications: medical imaging, non‑destructive testing.

Worked Example – Wavelength

A sound wave has a frequency of 500 Hz and travels in air at 340 m s⁻¹. Find its wavelength.

λ = v/f = 340/500 = 0.68 m.

AO Mapping (Waves)

4. Electricity & Magnetism

Electricity Basics

• Charge q (C), current I = Δq/Δt (A).
• Potential difference V (V), resistance R (Ω), Ohm’s law V = IR.
• Power: P = VI = I²R = V²/R (W).
• Series circuits: ΣR, same I, V splits.
• Parallel circuits: 1/ΣR, same V, I splits.
• Energy transferred: W = VIt = Pt (J).

Magnetism & Electromagnetism

• Magnetic field lines; Earth’s magnetic field (horizontal component ≈ 25 µT).
• Force on a moving charge: F = qvB sinθ.
• Force on a current‑carrying conductor: F = BIL sinθ.
• Electromagnetic induction:

  • Faraday’s law: induced emf = –ΔΦ/Δt.
  • Lenz’s law: direction opposes the change producing it.

• Transformers: \(Vs/Vp = Ns/Np\); \(Is/Ip = Np/Ns\).
• Generators & motors – principle of rotating a coil in a magnetic field.

Worked Example – Circuit Resistance

Find the total resistance of a 4 Ω resistor in series with a parallel combination of 6 Ω and 12 Ω.

Parallel part: \(1/Rp = 1/6 + 1/12 = 3/12 ⇒ Rp = 4 Ω\).

Total \(R = 4 Ω + 4 Ω = 8 Ω\).

AO Mapping (Electricity & Magnetism)

5. Nuclear Physics

Atomic Structure

• Protons, neutrons, electrons; atomic number Z, mass number A.
• Isotopes – same Z, different A.
• Stable vs. unstable nuclei; binding energy concept (qualitative).

Radioactivity

• α‑particles (He²⁺, +2 e, low penetration), β‑particles (electrons, moderate penetration), γ‑rays (photons, high penetration).
• Half‑life t½ and decay constant λ:

  \[

  N = N0 e^{-λt},\qquad t{½} = \frac{\ln2}{λ}

  \]

• Activity A = λN (Bq).
• Applications: medical imaging (PET, radiotherapy), carbon dating, smoke detectors.

Safety & Protection

• Time‑distance‑shielding principle.
• Shielding materials: α → paper, β → aluminium, γ → lead or concrete.
• ALARA – keep exposure “as low as reasonably achievable”.

Worked Example – Half‑Life

A 80 g sample has a half‑life of 5 years. How much remains after 15 years?

Number of half‑lives = 15/5 = 3.

Remaining mass = 80 × (½)³ = 80 × 0.125 = 10 g.

AO Mapping (Nuclear Physics)

6. Space Physics

6.1 Gravitational Field Strength

• Definition: Gravitational field strength (g) = force per unit mass, g = F/m (units m s⁻²).
• Surface gravity of a spherical planet:

  \[

  g_{\text{surface}} = \frac{GM}{R^{2}}

  \]

  where G = 6.67×10⁻¹¹ N m² kg⁻², M = planetary mass, R = radius.

• Dependence on mass: For planets of similar size, a larger mass directly increases g. If radius also changes, the effect is governed by the ratio M/R².
• Inverse‑square law for any point outside the planet:

  \[

  g(r) = \frac{GM}{r^{2}} = g_{0}\left(\frac{R}{r}\right)^{2}

  \]

  where r = distance from the planet’s centre.

• Effect of distance: Doubling the distance reduces g to one‑quarter; tripling reduces it to one‑ninth, etc.

Worked Example – Height Above Earth

Find the gravitational field strength 400 km above Earth’s surface.

• Given: g₀ = 9.81 m s⁻², R = 6.37×10⁶ m, h = 4.0×10⁵ m.
• r = R + h = 6.77×10⁶ m

• \[

  g = g_{0}\left(\frac{R}{R+h}\right)^{2}

  = 9.81\left(\frac{6.37×10^{6}}{6.77×10^{6}}\right)^{2}

  \approx 8.7\ \text{m s}^{-2}

  \]

6.2 Earth’s Rotation & Orbit

• Rotation period = 24 h → apparent daily motion, Coriolis effect on moving objects.
• Orbit period = 365.25 days; axial tilt = 23.5° gives seasons.
• Escape velocity:

  \[

  v_{\text{esc}} = \sqrt{\frac{2GM}{R}}

  \]

  (≈ 11.2 km s⁻¹ for Earth).

6.3 Additional Space Topics (Extended)

• Kepler’s Laws (qualitative) – elliptical orbits, equal areas in equal times, period‑radius relationship.
• Satellite motion – balance of gravitational force and centripetal force:

  \[

  \frac{GMm}{r^{2}} = \frac{mv^{2}}{r}

  \]

  leading to \(v = \sqrt{GM/r}\).

• Energy in orbital motion – total mechanical energy \(E = -\frac{GMm}{2r}\).

AO Mapping (Space Physics)

7. Practical Skills & Experiment Ideas

• Design and analyse a force‑plate experiment to determine the coefficient of static friction for different surfaces.
• Investigate torque using a lever and varying load distances – verify τ = Fr sinθ.
• Measure spring constant from load‑extension graphs; identify the limit of proportionality.
• Quantify conduction through metal, wood and plastic rods using a heat‑flow apparatus; calculate thermal conductivity k.
• Determine convection coefficient by heating water in a beaker with and without stirring; use Q = hAΔT.
• Use a black‑body furnace and a thermopile to verify the Stefan‑Boltzmann law.
• Set up a simple pendulum to explore circular motion and centripetal force concepts.
• Carry out a radioactive decay measurement with a Geiger‑Müller tube; plot activity versus time and extract half‑life.
• Build a small satellite model (mass on string) to demonstrate balance of gravitational and centripetal forces.
• Perform a laser‑diffraction experiment to observe interference patterns and calculate wavelength.

Data‑handling & Uncertainty

• Use percentage uncertainty: \(\%Δ = (Δx/x)×100\).
• Propagation of uncertainties for multiplication/division: add percentage uncertainties.
• Graphical determination of gradients (e.g., g from a falling‑ball distance‑time graph).

8. Summary Checklists & Quick Reference

Motion, Forces & Energy – Quick Formulas

Thermal Physics – Quick Formulas

Space Physics – Quick Formulas

AO Checklist – What to Remember for the Exam

• Identify which formula applies (e.g., choose between kinetic and potential energy).
• Check units and convert where necessary (e.g., km → m, °C → K).
• State assumptions clearly (e.g., neglect air resistance, treat planet as a perfect sphere).
• Show all steps – marks are awarded for method as well as final answer.
• For practical questions, include a brief description of the set‑up, variables measured, and how uncertainties are evaluated.