Define the Hubble constant H_0 as the ratio of the speed at which the galaxy is moving away from the Earth to its distance from the Earth; recall and use the equation H_0 = v / d

Cambridge IGCSE Physics (0625) – Concise Syllabus Notes

Learning Objectives (Assessment Objectives)

• AO1 – Knowledge & Understanding: Define key concepts, recall formulae, and explain underlying principles across all six core strands.
• AO2 – Application & Problem‑Solving: Use equations, diagrams and logical reasoning to solve quantitative and qualitative questions.
• AO3 – Experimental Skills: Plan, carry out and evaluate investigations; analyse data; recognise sources of error and uncertainty.

1 Motion, Forces & Energy

1.1 Key Concepts

• Scalars & Vectors: speed, distance (scalar); velocity, displacement (vector). Resultant of two vectors (graphical tip‑to‑tail method).
• Kinematics: v = s/t, a = Δv/Δt, equations of motion for constant acceleration (v = u + at, s = ut + ½at², v² = u² + 2as).
• Forces: weight, normal, tension, friction (solid & fluid), resultant force, Newton’s three laws.
• Moments & Centre of Gravity: moment = F × perpendicular distance; centre of gravity = point of application of resultant weight.
• Circular Motion: centripetal force F = mv²/r, period T = 2πr/v.
• Impulse & Momentum: impulse = FΔt = Δp, momentum p = mv.
• Work, Energy & Power: W = F s cosθ, kinetic energy Ek = ½mv², gravitational potential energy Epg = mgh, elastic potential energy = ½kx², power P = W/t = Fv.
• Energy Resources & Efficiency: renewable (solar, wind, hydro) vs non‑renewable (fossil fuels, nuclear); efficiency η = useful energy output / total energy input × 100 %.
• Pressure & Density: pressure p = F/A, density ρ = m/V.

1.2 Formulae & Units

1.3 Worked Example (AO2)

A 1500 kg car accelerates uniformly from 0 to 25 m s⁻¹ in 8 s. Determine:

1. Acceleration
2. Net force acting on the car
3. Kinetic energy at 25 m s⁻¹
4. Power delivered if the acceleration is constant.

Solution

1. a = Δv/Δt = 25/8 = 3.13 m s⁻²
2. F = ma = 1500 × 3.13 ≈ 4.7 × 10³ N
3. E_k = ½ mv² = 0.5 × 1500 × 25² = 4.69 × 10⁵ J
4. Power = work/time = E_k / t = 4.69 × 10⁵ J / 8 s ≈ 5.9 × 10⁴ W

1.4 Practical Skill (AO3)

Investigation – Determining the coefficient of kinetic friction. A wooden block on a horizontal track is pulled by a hanging mass attached to a string over a pulley. Vary the hanging mass, record acceleration with a motion sensor, and use F = ma to calculate μk = Ff/N. Discuss sources of error (air resistance, pulley friction, string mass).

2 Thermal Physics

2.1 Key Concepts

• Particle model – temperature reflects average kinetic energy of particles.
• Temperature scales: Celsius (°C), Kelvin (K) (K = °C + 273.15).
• Specific heat capacity (c) – Q = mcΔT.
• Latent heat (L) – phase change without temperature change: Q = mL (Lfusion, Lvapour).
• Thermal expansion: linear ΔL = αL₀ΔT, volumetric ΔV = βV₀ΔT (β ≈ 3α for solids).
• Conduction – kinetic theory, lattice vibrations (metals) vs free‑electron conduction.
• Convection – density differences, circulation currents; quantitative description using ρ g Δh.
• Radiation – emission of electromagnetic waves; qualitative discussion of emissivity and the Stefan‑Boltzmann law (P ∝ T⁴).
• Ideal gas behaviour – pV = nRT, relationship between temperature and kinetic energy.
• Energy resources – renewable (solar, wind, hydro, tidal) and non‑renewable (coal, oil, natural gas, nuclear). Environmental impact.

2.2 Formulae & Units

2.3 Worked Example (AO2)

How much heat is required to melt 0.500 kg of ice at –10 °C and then raise the resulting water to 30 °C? (cice = 2100 J kg⁻¹ K⁻¹, cwater = 4200 J kg⁻¹ K⁻¹, L_fusion = 3.34 × 10⁵ J kg⁻¹.)

Solution:

1. Heat to warm ice to 0 °C: Q₁ = mcΔT = 0.5 × 2100 × 10 = 1.05 × 10⁴ J.
2. Heat to melt ice: Q₂ = mL_f = 0.5 × 3.34 × 10⁵ = 1.67 × 10⁵ J.
3. Heat to raise water from 0 °C to 30 °C: Q₃ = mcΔT = 0.5 × 4200 × 30 = 6.30 × 10⁴ J.
4. Total Q = Q₁ + Q₂ + Q₃ ≈ 2.40 × 10⁵ J.

2.4 Practical Skill (AO3)

Calorimetry – Determining the specific heat capacity of an unknown metal. Heat a known mass of metal in boiling water, transfer it to a calorimeter containing a known mass of water at a lower temperature, record the equilibrium temperature, and use Qmetal + Qwater = 0 (neglecting calorimeter heat capacity). Evaluate heat losses and discuss systematic errors.

3 Waves

3.1 Key Concepts

• Wave terminology: crest, trough, wavelength λ, period T, frequency f (f = 1/T), amplitude, phase.
• Wave speed: v = fλ (applicable to all mechanical waves).
• Transverse vs longitudinal waves: direction of particle motion relative to wave propagation.
• Reflection & Refraction: angle of incidence = angle of reflection; Snell’s law n₁ sinθ₁ = n₂ sinθ₂, where n = c/v.
• Diffraction: bending around obstacles; significant when aperture size ≈ λ.
• Interference: constructive (Δφ = 0, 2π…) and destructive (Δφ = π, 3π…) patterns; double‑slit formula d sinθ = nλ.
• Sound: 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.
• Ultrasound applications: medical imaging, non‑destructive testing.
• Light & Optics: electromagnetic wave, visible spectrum 400–700 nm; lenses (convex/concave), mirror equation 1/f = 1/do + 1/di, magnification m = hi/ho = –di/do.
• Electromagnetic spectrum: radio, microwave, infrared, visible, ultraviolet, X‑ray, γ‑ray – typical uses and hazards.

3.2 Formulae & Units

3.3 Worked Example (AO2)

A double‑slit apparatus uses monochromatic light of wavelength 600 nm. The slits are 0.30 mm apart. On a screen 2.0 m away, the bright fringe of order n = 3 is observed. Find the distance of this fringe from the central maximum.

Solution:

1. Path‑difference condition: d sinθ = nλ → sinθ = nλ/d = (3 × 600 × 10⁻⁹)/(0.30 × 10⁻³) = 0.006.
2. θ ≈ sinθ = 0.006 rad (small‑angle approximation).
3. Linear displacement y = L tanθ ≈ L sinθ = 2.0 × 0.006 = 0.012 m = 12 mm.

3.4 Practical Skill (AO3)

Ripple‑tank investigation of diffraction. Generate plane water waves, place a rectangular slit of variable width, measure the spread of the diffracted pattern with a ruler, and compare observed angles with the single‑slit condition a sinθ = mλ. Discuss limitations (wave damping, measurement error).

4 Electricity & Magnetism

4.1 Key Concepts

• Charge (q), current (I = ΔQ/Δt), potential difference (V), resistance (R), resistivity (ρ).
• Ohm’s law (V = IR) and power (P = VI = I²R = V²/R).
• Series and parallel circuits – equivalent resistance, current division, voltage division.
• Electromotive force (e.m.f.) and internal resistance (r) – terminal voltage V = ε – Ir.
• Energy transfer – Joule heating (Q = I²Rt), electrical energy E = VIt.
• Magnetic fields: field lines, Earth’s field, right‑hand rule for straight conductors.
• Force on a current‑carrying conductor: F = BIl sinθ.
• Electromagnetic induction – Faraday’s law ε = –ΔΦ/Δt, Lenz’s law, applications (generators, transformers, induction cookers).
• Safety devices – fuses, circuit breakers, earthing, insulation.

4.2 Formulae & Units

4.3 Worked Example (AO2)

A 12 V battery with internal resistance 0.5 Ω supplies a lamp of resistance 4 Ω. Find the terminal voltage across the lamp and the power dissipated in the lamp.

Solution:

1. Total resistance Rtotal = Rlamp + r = 4 + 0.5 = 4.5 Ω.
2. Current I = ε / R_total = 12 / 4.5 = 2.67 A.
3. Terminal voltage Vlamp = I Rlamp = 2.67 × 4 ≈ 10.7 V.
4. Power in lamp P = V_lamp I = 10.7 × 2.67 ≈ 28.6 W.

4.4 Practical Skill (AO3)

Investigating internal resistance of a cell. Connect a cell to a variable resistor, measure V and I for several resistance values, plot V against I, and determine ε (y‑intercept) and r (negative slope). Discuss how temperature and age of the cell affect r.

5 Nuclear Physics

5.1 Key Concepts

• Structure of the atom – protons, neutrons, electrons; isotopes (same Z, different N).
• Radioactive decay types: α (He‑2 nucleus), β⁻ (electron), β⁺ (positron), γ (high‑energy photon).
• Decay law: N = N₀e⁻λt, half‑life t½ = ln 2 / λ.
• Activity A = λN (Bq).
• Mass–energy equivalence (E = mc²) – binding energy, mass defect.
• Fission (heavy nuclei split, release neutrons) and fusion (light nuclei combine, release energy).
• Applications: medical imaging (X‑ray, PET), radiocarbon dating, nuclear power, smoke detectors.
• Safety and protection – shielding (lead, concrete), distance, time, ALARA principle.

5.2 Formulae & Units

5.3 Worked Example (AO2)

A 2.0 g sample of ^226Ra (t½ = 1600 y) decays by α‑emission. Calculate the activity in becquerels.

Solution:

1. Number of atoms N₀ = (mass / M) × N_A = (2.0 × 10⁻³ kg / 0.226 kg mol⁻¹) × 6.02 × 10²³ ≈ 5.33 × 10²¹ atoms.
2. Convert half‑life to seconds: t½ = 1600 y × 365 d × 24 h × 3600 s ≈ 5.05 × 10¹⁰ s.
3. λ = ln 2 / t½ ≈ 1.37 × 10⁻¹¹ s⁻¹.
4. Activity A = λN₀ ≈ 1.37 × 10⁻¹¹ × 5.33 × 10²¹ ≈ 7.3 × 10¹⁰ Bq.

5.4 Practical Skill (AO3)

Geiger‑Müller counting of a weak β‑source. Record counts every 30 s for 5 min, plot ln (count) against time, determine λ from the slope, and calculate the half‑life. Discuss background radiation, dead‑time correction, and statistical (Poisson) uncertainties.

6 Space Physics & Cosmology

6.1 Fundamentals of the Solar System

• Earth’s rotation (24 h) → day/night; axial tilt (23.5°) → seasons.
• Orbital motion: period 365.25 d, average orbital speed ≈ 30 km s⁻¹, centripetal force provided by gravity (F = GMm/r²).
• Kepler’s laws (qualitative): elliptical orbits, equal areas in equal times, P² ∝ a³.
• Escape velocity: vₑ = √(2GM/r). For Earth vₑ ≈ 11.2 km s⁻¹.
• Satellites: geostationary orbit (≈ 35 800 km, period 24 h), low‑Earth orbit (≈ 200–2000 km). Applications – communications, weather, GPS.
• Gravitational field strength g = GM/r²; variation with altitude.
• Tides – caused by differential lunar/solar gravity; spring and neap tides.

6.2 Cosmology – The Expanding Universe

Hubble’s Law

Spectral lines from distant galaxies are shifted towards longer wavelengths (red‑shift). The red‑shift, z, is defined as

\[

z = \frac{\Delta\lambda}{\lambda_0}

\]

For velocities much less than the speed of light, the recession velocity v is approximated by

\[

v \approx cz

\]

where c = 3.00 × 10⁵ km s⁻¹.

Hubble’s constant (H₀) is defined as the ratio of recession velocity to distance:

\[

H_0 = \frac{v}{d}

\]

Typical IGCSE‑level value: H₀ ≈ 70 km s⁻¹ Mpc⁻¹ (1 Mpc = 3.09 × 10¹⁹ km). The relation implies that the farther a galaxy is, the faster it appears to recede – evidence for an expanding universe.

Implications of H₀

• Age of the Universe (simplified) ≈ 1/H₀ ≈ 14 billion years.
• Linear relationship forms the basis of the distance ladder (Cepheid variables, supernovae).
• Cosmic Microwave Background (CMB) provides supporting evidence for the Big Bang.

6.3 Formulae & Units (Space & Cosmology)

6.4 Worked Example (AO2)

A galaxy shows a spectral line at 660 nm, whereas the same line in the laboratory is at 656 nm. Calculate the recession velocity and estimate the distance using H₀ = 70 km s⁻¹ Mpc⁻¹.

Solution:

1. Red‑shift: z = (660 – 656)/656 = 0.00610.
2. Recession velocity: v = cz = 3.00 × 10⁵ km s⁻¹ × 0.00610 ≈ 1.83 × 10³ km s⁻¹.
3. Distance: d = v / H₀ = 1.83 × 10³ / 70 ≈ 26 Mpc.

6.5 Practical Skill (AO3)

Determining H₀ from a set of galaxy data. Using a table of red‑shifts and known distances (derived from Cepheid variables), plot recession velocity v against distance d, draw the best‑fit straight line, and determine the gradient as H₀. Discuss sources of error (uncertainty in distance measurements, peculiar velocities, instrumental calibration).

Summary of AO Alignment

• AO1: All definitions, formulas and conceptual explanations are presented.
• AO2: Worked examples illustrate the application of each formula to typical exam‑style questions.
• AO3: Each strand includes a practical investigation that can be performed with typical school‑lab equipment, with prompts for error analysis.

Use these notes as a quick‑reference revision tool, but always practise past‑paper questions and conduct the suggested investigations to consolidate understanding and develop the skills required for the Cambridge IGCSE Physics (0625) examination.