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QCE · QCE Units 3 & 4

Physics

Gravity, electromagnetism and revolutions in modern physics — full Paper 1 + Paper 2 practice External Assessments with worked solutions.

20full-length model exams with mark-by-mark answer guides
20detailed note sets — ~120 pages across every topic
64exam-style practice questions with worked solutions
60flashcards for every key term & formula
Allofficial past papers

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Sample revision note

Circular motion fundamentals

1. What is uniform circular motion?

An object undergoing uniform circular motion travels in a circular path at constant speed. Although the magnitude of velocity is constant, the direction changes continuously — which means the velocity vector is always changing. By Newton's first law, a changing velocity requires a net force. This is the central idea underpinning all circular motion analysis in Unit 3.

It is critical to distinguish speed (scalar, constant in UCM) from velocity (vector, continuously changing in UCM). A common misconception is that "constant speed" implies "no acceleration" — this is false. Acceleration is defined as the rate of change of velocity, and because direction changes, there is always acceleration present.

Key kinematic quantities for UCM:

  • Period (T): time taken for one complete revolution, measured in seconds (s).
  • Frequency (f): number of revolutions per second, measured in hertz (Hz = s⁻¹). Related by f = 1/T.
  • Angular speed (ω): rate of change of angular displacement, in rad s⁻¹. Given by ω = 2π/T = 2πf.
  • Linear (tangential) speed (v): the instantaneous speed along the circular path, in m s⁻¹. Given by v = 2πr/T, where r is the radius of the circle in metres.

Worked example: A car travels around a roundabout of radius 12 m and completes one full loop in 8.0 s. Find its speed.
v = 2πr/T = 2π × 12 / 8.0 ≈ 9.42 m s⁻¹

This speed is constant throughout the motion (assuming UCM), but the direction of the velocity vector rotates through 360° each period.

2. Centripetal acceleration — derivation and formula

Because the velocity direction changes continuously in UCM, there must be an acceleration directed toward the centre of the circle. This is called centripetal acceleration (from Latin centrum = centre, petere = to seek). It is always directed radially inward — toward the centre of the circular path — and is therefore perpendicular to the velocity at every instant.

The two equivalent expressions for centripetal acceleration are:

  • ac = v² / r  (using linear speed and radius)
  • ac = 4π²r / T²  (using radius and period — derived by substituting v = 2πr/T)

Unit analysis: For ac = v²/r: units are (m s⁻¹)² / m = m² s⁻² / m = m s⁻². For ac = 4π²r/T²: units are m / s² = m s⁻². Both expressions give SI units of m s⁻², consistent with acceleration. Note that 4π² is dimensionless.

Direction convention (QCAA): Centripetal acceleration is defined as pointing toward the centre of the circular path. This direction changes continuously as the object moves around the circle. It is never tangential and never outward. Do not describe it as pointing "upward" or "downward" in general — state specifically "toward the centre" or use a diagram showing the inward radial direction.

Worked example — Brisbane Story Bridge climb: Tourists on a Story Bridge climb walk across an arc of radius approximately 30 m at a constant speed of 1.2 m s⁻¹ (extremely slow stroll). Find the centripetal acceleration.
ac = v²/r = (1.2)²/30 = 1.44/30 = 0.048 m s⁻²
This is tiny compared to g = 9.8 m s⁻², confirming that for slow motion on gentle curves, centripetal effects are negligible.

Worked example — motor racing at Queensland Raceway: A racing car takes a bend of radius 80 m at 60 m s⁻¹. Find the centripetal acceleration and express it as a multiple of g.
ac = v²/r = (60)²/80 = 3600/80 = 45 m s⁻²
45 / 9.8 ≈ 4.6g
Drivers experience approximately 4.6 times their body weight directed horizontally toward the centre of the turn — a significant physiological load.

Sample exam question

A communications satellite is held in geostationary orbit above a fixed point in Queensland. Which statement correctly describes its motion?

  • Its orbital period is exactly 12 hours and it passes over Queensland twice per day
  • Its orbital period is approximately 24 hours, matching Earth's rotation, so it stays above the same point
  • It is stationary in space and does not move relative to the distant stars
  • It travels in a polar orbit, passing over both poles once each day
Show the worked answer

Answer: A

B

All 20 practice exams

  1. Exam 1 — Unit 3 Gravity and Electromagnetism: uniform circular motion and centripetal dynamics, Newton's Law of Universal Gravitation, gravitational field strength, Kepler's three laws, orbital speed and satellite mechanics (geostationary orbit above Queensland), Coulomb's Law and electric fields, work on charges, the motor effect, electromagnetic induction (Faraday/Lenz), transformers and power transmission; Unit 4 Revolutions in Modern Physics: special relativity (postulates, simultaneity, time dilation, length contraction, mass-energy equivalence), quantum theory (Planck, photoelectric effect, de Broglie duality, Bohr hydrogen model), Standard Model (quarks, leptons, baryons, mesons, antiparticles, fundamental forces and exchange bosons, conservation laws, Feynman diagrams); QCAA EA format: Paper 1 (Section A 20 MCQ = 20 marks; Section B short/extended response = 28 marks) and Paper 2 (Section C stimulus-based short/extended response = 49 marks); grand total 97 marks
  2. Exam 2 — Special relativity (Lorentz factor, time dilation, length contraction, simultaneity, relativistic momentum/energy, mass-energy equivalence) anchored to a 0.85c interstellar voyage to Alpha Centauri; Unit 3 Gravity and Electromagnetism: uniform circular motion, Newton's law of universal gravitation, gravitational field strength, Kepler's three laws, orbital/satellite mechanics; Unit 3 electromagnetism: Coulomb's law, electric fields, work on charges, the motor effect (F=BIL and F=qvB), electromagnetic induction (Faraday/Lenz), AC generators, transformers and power transmission
  3. Exam 3 — Unit 3 Gravity & Electromagnetism: uniform circular motion, Newton's gravitation, gravitational field strength, Kepler's laws, orbital/satellite mechanics, Coulomb's Law, electric fields, work on charges, motor effect, electromagnetic induction (Faraday & Lenz), AC generators, transformers & power transmission; Unit 4 Revolutions in Modern Physics: special relativity (postulates, simultaneity, time dilation, length contraction, mass-energy equivalence), quantum theory (Planck, photoelectric effect, de Broglie duality, Bohr hydrogen model), Standard Model (quarks, leptons, baryons, mesons, antiparticles, four forces & exchange bosons, conservation laws, Feynman diagrams); Stimulus thread: a charged oil droplet suspended motionless between parallel plates (Millikan-style) - calculating electric field strength E=V/d, charge q from force balance qE=mg, number of excess electrons, and work done W=qV moving the droplet between plates
  4. Exam 4 — Unit 3 Gravity and Electromagnetism: uniform circular motion and centripetal dynamics, Newton's Law of Universal Gravitation, gravitational field strength, Kepler's three laws, orbital/satellite mechanics, Coulomb's Law, electric fields, work done on charges, the motor effect, electromagnetic induction (Faraday/Lenz), AC generators, and transformers with power transmission; Unit 4 Revolutions in Modern Physics: special relativity (Einstein's postulates, simultaneity, time dilation, length contraction, mass-energy equivalence), quantum theory (Planck's hypothesis, photoelectric effect, de Broglie duality, Bohr hydrogen model), and the Standard Model (quarks, leptons, baryons, mesons, antiparticles, four forces and exchange bosons, conservation laws, Feynman diagrams); Cosmic-ray muon stimulus thread: applying time dilation in the Earth frame and length contraction in the muon rest frame to explain why muons reach sea level despite a short half-life, with quantitative survival-fraction reasoning that reconciles both frames
  5. Exam 5 — Unit 3: electromagnetic induction (Faraday's and Lenz's Laws), AC generators, transformers and power transmission, motor effect, Coulomb's Law and electric fields, work on charges, circular motion, gravitation, Kepler's laws and orbital mechanics; Unit 4: special relativity (time dilation, length contraction, mass-energy equivalence), quantum theory (photoelectric effect, de Broglie wavelength, Bohr hydrogen model, Planck's hypothesis), Standard Model (quarks, leptons, baryons/mesons, exchange bosons, conservation laws, Feynman diagrams); Context thread: a wind turbine generator supplying a remote Queensland farm via electromagnetic induction and transformer step-up for grid transmission
  6. Exam 6 — Unit 3 Gravity & Electromagnetism: circular motion, Newton's gravitation, Kepler's laws, orbital mechanics, Coulomb's law, electric fields, motor effect, electromagnetic induction (Faraday/Lenz), AC generators, transformers & power transmission; Unit 4 Revolutions in Modern Physics: special relativity (postulates, simultaneity, time dilation, length contraction, mass-energy), quantum theory (Planck, photoelectric effect, de Broglie, Bohr model), Standard Model (quarks, leptons, baryons/mesons, fundamental forces & bosons, conservation laws, Feynman diagrams); Core stimulus: solar-panel photoelectric experiment — UV light of varying frequency on a metal surface, stopping-voltage measurements, Ek-f graph analysis to extract work function W (= 3.32e-19 J, 2.07 eV) and threshold frequency f0 (= 5.0e14 Hz, gradient = h = 6.63e-34 J s)
  7. Exam 7 — QCAA Physics Units 3 & 4 (General, 2025 v1.3) full External Assessment, contextualised around the Large Hadron Collider; Unit 3 Gravity & Electromagnetism: uniform circular motion, Newton's gravitation, gravitational field strength, Kepler's laws, orbital/satellite speed, Coulomb's law and electric fields, work on charges, motor effect, F=qvB, electromagnetic induction (Faraday/Lenz), AC generators, transformers and power transmission; Unit 4 Revolutions in Modern Physics: special relativity (postulates, simultaneity, time dilation, length contraction, mass-energy equivalence), quantum theory (Planck, photoelectric effect, de Broglie, Bohr hydrogen model), Standard Model (quarks/leptons, baryons/mesons, antiparticles, four forces and exchange bosons, conservation laws, Feynman diagrams)
  8. Exam 8 — Unit 3: uniform circular motion and centripetal force; Unit 3: Newton's Law of Universal Gravitation and gravitational field strength; Unit 3: Kepler's laws, orbital mechanics and satellite speed (incl. geostationary orbits)
  9. Exam 9 — MRI superconducting magnets as the stimulus thread: force on a current-carrying wire (F = BIL), the motor effect, torque on coil, and quantitative contrast with Earth's ~5x10^-5 T field; Unit 3 Gravity and Electromagnetism: uniform circular motion and centripetal dynamics, Newton's Law of Universal Gravitation, gravitational field strength, Kepler's three laws, orbital/satellite speed; Coulomb's Law, electric fields, and work done on charges; the motor effect on conductors and moving charges (F = BIL, F = qvB)
  10. Exam 10 — Unit 4 quantum theory anchored on de Broglie electron diffraction through a crystal lattice and comparison to X-ray Bragg diffraction; de Broglie wavelength from accelerating voltage, momentum and kinetic energy of accelerated electrons; Bragg's law nλ = 2d sinθ: multi-order diffraction, electron vs X-ray diffraction angles, crystal lattice spacing determination
  11. Exam 11 — QCAA Physics Units 3 & 4 (General, 2025 v1.3) External Assessment; Unit 3: uniform circular motion and centripetal dynamics, Newton's Law of Universal Gravitation, gravitational field strength, Kepler's three laws, orbital/satellite mechanics, Coulomb's Law and electric fields, work done on charges, the motor effect, electromagnetic induction (Faraday/Lenz), AC generators, transformers and power transmission; Unit 4: special relativity (postulates, simultaneity, time dilation, length contraction, mass-energy equivalence), quantum theory (Planck, photoelectric effect, de Broglie, Bohr model), Standard Model (quarks/leptons, baryons/mesons, antiparticles, four forces and exchange bosons, conservation laws, Feynman diagrams)
  12. Exam 12 — QCAA Physics Units 3 & 4 (General, 2025 v1.3) External Assessment - Practice EA 12 of 20; Stimulus thread: HVDC power transmission across regional Queensland - I-squared-R losses, step-up transformers, Faraday's Law; Unit 3 Gravity & Electromagnetism: circular motion, gravitation, Kepler, orbits, Coulomb's Law, electric fields, motor effect, induction, AC generators, transformers, power transmission
  13. Exam 13 — QCAA Physics Units 3 and 4 (General, 2025 v1.3) full practice External Assessment (Practice EA 13 of 20); Unit 3 Gravity and Electromagnetism: uniform circular motion and centripetal force, Newton's Law of Universal Gravitation, gravitational field strength and Kepler's laws, orbital and satellite mechanics, Coulomb's Law and electric fields, work done on charges, the motor effect (force on conductors and moving charges), electromagnetic induction (Faraday's and Lenz's Laws), AC generators, transformers and power transmission; Unit 4 Revolutions in Modern Physics: special relativity (two postulates, simultaneity, time dilation, length contraction, mass-energy equivalence), quantum theory (Planck's hypothesis, photoelectric effect, de Broglie wave-particle duality, Bohr hydrogen atom), the Standard Model (quarks and leptons, baryons and mesons, antiparticles, four fundamental forces and exchange bosons, conservation laws, Feynman diagrams)
  14. Exam 14 — Unit 4 Standard Model: electron-positron annihilation, Feynman diagrams, exchange bosons, conservation laws, quark/lepton classification; Unit 4 Special Relativity: time dilation, length contraction, mass-energy equivalence, muon decay evidence; Unit 4 Quantum: photoelectric effect, Planck's hypothesis, de Broglie duality, Bohr hydrogen model
  15. Exam 15 — QCAA Physics Units 3 & 4 (General, 2025 v1.3) Practice External Assessment 15 of 20; Stimulus context: a probe descending into a deep gravity well near a 12-solar-mass star — gravitational field strength vs radius, orbital/satellite speed, Kepler's laws, and relativistic length contraction at final orbital speed; Unit 3 — Gravity and Electromagnetism: uniform circular motion and centripetal dynamics, Newton's Law of Universal Gravitation, gravitational field strength, Kepler's three laws, orbital mechanics, Coulomb's Law and electric fields, work on charges, the motor effect, electromagnetic induction (Faraday's and Lenz's Laws), AC generators and transformers/power transmission
  16. Exam 16 — Unit 3 Gravity & Electromagnetism: Coulomb's Law, electric fields, work on charges, Newton's law of gravitation, gravitational field strength, Kepler's laws, orbital/satellite motion, uniform circular motion, motor effect, magnetic force on charges/conductors, Faraday's & Lenz's Laws, AC generators, transformers, power transmission; Unit 4 Revolutions in Modern Physics: special relativity (postulates, simultaneity, time dilation, length contraction, mass-energy equivalence), quantum theory (Planck, photoelectric effect, de Broglie duality, Bohr hydrogen model), Standard Model (quarks, leptons, baryons, mesons, antiparticles, fundamental forces & exchange bosons, conservation laws, Feynman diagrams); Stimulus context: a charged sphere rolled on a frictionless horizontal surface near a second charged sphere — applying Coulomb's Law, comparing the electric force to gravity between the same masses, and locating the equilibrium separation
  17. Exam 17 — Special relativity (Unit 4): Einstein's postulates, simultaneity, time dilation, length contraction, mass-energy equivalence - framed around a SpaceX Starship near-relativistic re-entry thought experiment; Quantum theory (Unit 4): Planck's hypothesis, photoelectric effect, de Broglie wave-particle duality, Bohr hydrogen model; Standard Model (Unit 4): quarks/leptons, baryons/mesons, antiparticles, four fundamental forces and exchange bosons, conservation laws, Feynman diagrams
  18. Exam 18 — Unit 3: uniform circular motion and centripetal force; Unit 3: Newton's Law of Universal Gravitation and gravitational field strength; Unit 3: Kepler's laws and orbital/satellite mechanics
  19. Exam 19 — Unit 3 Gravity and Electromagnetism: uniform circular motion and centripetal force, Newton's Law of Universal Gravitation and gravitational field strength, Kepler's three laws and orbital/satellite mechanics, Coulomb's Law and electric fields, work done on charges, the motor effect (F=BIL and F=qvB), electromagnetic induction via Faraday's and Lenz's Laws, AC generators, and transformer operation applied to power transmission; Unit 4 Revolutions in Modern Physics: special relativity (two postulates, simultaneity, time dilation, length contraction, mass-energy equivalence), quantum theory (Planck's hypothesis, photoelectric effect, de Broglie duality, Bohr hydrogen model), and the Standard Model (quarks, leptons, baryons/mesons, antiparticles, four fundamental forces and exchange bosons, conservation laws, Feynman diagrams); Stimulus context: a 330 kV to 240 V outback substation transformer (turns ratios, Lenz's Law in coil operation, current ratios at 100% efficiency) plus power-transmission loss analysis
  20. Exam 20 — Unit 3 Gravity and Electromagnetism: uniform circular motion, Newton's universal gravitation, gravitational field strength and Kepler's laws, orbital/satellite mechanics, Coulomb's law and electric fields, work on charges, motor effect, electromagnetic induction (Faraday/Lenz), AC generators, transformers and power transmission; Unit 4 Revolutions in Modern Physics: special relativity (postulates, simultaneity, time dilation, length contraction, mass-energy equivalence), quantum theory (Planck's hypothesis, photoelectric effect, de Broglie duality, Bohr hydrogen model), the Standard Model (quarks, leptons, baryons/mesons, antiparticles, four forces and exchange bosons, conservation laws, Feynman diagrams); Stimulus thread: a magnetically confined ionised-hydrogen plasma emitting a blackbody spectrum, used to contrast the classical Rayleigh-Jeans prediction with the Planck quantised spectrum, locate the peak wavelength via Wien's law, and identify the soft X-ray regime

All 20 revision notes

  • Circular motion fundamentals
  • Gravitational force between masses
  • Gravitational field strength
  • Kepler's Three Laws and Satellite Orbits
  • Energy in gravitational fields
  • Coulomb's Law and Electric Field Strength
  • Electric potential difference and work done on charges
  • Force on current-carrying conductors and moving charges
  • Induced EMF, Faraday's Law and Lenz's Law
  • AC Generators and Transformers
  • Einstein's Two Postulates and Inertial Frames
  • Relativistic time dilation and length contraction
  • E = mc² and Relativistic Momentum
  • Blackbody radiation, quantisation, and E = hf
  • Einstein's photoelectric effect and the photon model
  • de Broglie wavelength and matter waves
  • Bohr model, quantised energy levels, and atomic spectra
  • Quarks, leptons, baryons, mesons, and antiparticles
  • Four fundamental forces and gauge bosons
  • Conservation laws, particle interactions, and Feynman diagrams