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HSC · HSC Year 12

Physics

Advanced mechanics, electromagnetism, the nature of light and the universe — full HSC papers 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
8official past papers

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Sample revision note

Gravitational Fields and Orbital Mechanics

Newton's Law of Universal Gravitation

Every object with mass exerts an attractive gravitational force on every other object with mass. Newton quantified this observation in his Law of Universal Gravitation:

F = GMm / r²

where:

  • F = gravitational force (N)
  • G = Universal Gravitational Constant = 6.674 × 10⁻¹¹ N m² kg⁻²
  • M = mass of the larger body (kg)
  • m = mass of the smaller body (kg)
  • r = centre-to-centre separation between the two bodies (m)

Several features are worth noting for HSC purposes:

  • The force is always attractive — gravitational repulsion does not exist.
  • The force obeys an inverse-square law: doubling the separation reduces F by a factor of 4; tripling it reduces F by a factor of 9.
  • The force acts equally on both bodies (Newton's Third Law pair): Earth pulls the Moon with the same magnitude force as the Moon pulls Earth.
  • r is measured from centre to centre, not surface to surface. For a satellite orbiting at height h above Earth's surface (radius RE), use r = RE + h.

Worked Example 1 — Force between Earth and Moon

Given: MEarth = 5.972 × 10²⁴ kg, MMoon = 7.342 × 10²² kg, r = 3.844 × 10⁸ m.

Step 1 — Write the formula: F = GMm / r²

Step 2 — Substitute values:

F = (6.674 × 10⁻¹¹) × (5.972 × 10²⁴) × (7.342 × 10²²) / (3.844 × 10⁸)²

Step 3 — Numerator: 6.674 × 5.972 × 7.342 = 6.674 × 43.82 ≈ 292.4; combine powers: 10⁻¹¹ × 10²⁴ × 10²² = 10³⁵; numerator ≈ 2.924 × 10³⁷

Step 4 — Denominator: (3.844)² = 14.776; (10⁸)² = 10¹⁶; denominator ≈ 1.478 × 10¹⁷

Step 5 — Divide: F ≈ 2.924 × 10³⁷ / 1.478 × 10¹⁷ ≈ 1.978 × 10²⁰ N

Result: F ≈ 1.98 × 10²⁰ N (consistent with the accepted value of ~1.98 × 10²⁰ N). Units check: N m² kg⁻² × kg × kg / m² = N. ✓

Gravitational Field Strength

Rather than always computing forces between pairs of masses, physicists use the concept of a gravitational field. A field exists at every point in space around a massive object; it describes the force that would act on a unit mass placed at that point.

The gravitational field strength g at a distance r from the centre of mass M is:

g = GM / r²

Units: N kg⁻¹ (equivalent to m s⁻²). At Earth's surface, g ≈ 9.8 N kg⁻¹.

Key relationships:

  • The force on a mass m placed in the field is F = mg, which — when expanded — returns F = GMm/r².
  • g decreases with the square of distance from the centre: moving from Earth's surface to twice Earth's radius reduces g to one-quarter.
  • g is a vector directed towards the centre of the source mass.

Worked Example 2 — Field strength at altitude

The International Space Station orbits at approximately h = 4.00 × 10⁵ m above Earth's surface. Calculate the gravitational field strength at that altitude.

Given: G = 6.674 × 10⁻¹¹ N m² kg⁻², ME = 5.972 × 10²⁴ kg, RE = 6.371 × 10⁶ m.

Step 1 — Find orbital radius: r = RE + h = 6.371 × 10⁶ + 4.00 × 10⁵ = 6.771 × 10⁶ m

Step 2 — Apply formula: g = GM/r² = (6.674 × 10⁻¹¹ × 5.972 × 10²⁴) / (6.771 × 10⁶)²

Step 3 — Numerator: 6.674 × 5.972 = 39.85; combine powers: 10⁻¹¹⁺²⁴ = 10¹³; numerator ≈ 3.985 × 10¹⁴

Step 4 — Denominator: (6.771)² = 45.85; (10⁶)² = 10¹²; denominator ≈ 4.585 × 10¹³

Step 5 — g ≈ 3.985 × 10¹⁴ / 4.585 × 10¹³ ≈ 8.69 N kg⁻¹

Result: g ≈ 8.69 N kg⁻¹ at ISS altitude. This is about 89% of the surface value — astronauts are not weightless because gravity is absent; they are in continuous free-fall around Earth (apparent weightlessness).

Sample exam question

A projectile is launched from level ground at 28 m/s at an angle of 35 degrees above the horizontal. Taking g = 9.8 m/s^2 and ignoring air resistance, what is the total time of flight before it returns to ground level?

  • A. 1.64 s
  • B. 2.34 s
  • C. 3.28 s
  • D. 4.67 s
Show the worked answer

Answer: C

Initial vertical velocity = 28 sin35 = 16.06 m/s. Time of flight = 2v_y/g = 2(16.06)/9.8 = 3.28 s.

All 20 practice exams

  1. Exam 1 — Advanced Mechanics (projectile, circular/banked, orbital gravitation) — the emphasised strand; Electromagnetism (motor torque, transformers/induction, parallel-conductor force + Lenz's law); The Nature of Light (special relativity, photoelectric effect, Planck graph analysis)
  2. Exam 2 — Electromagnetism (motor effect, induction, transformers, charged-particle motion) — primary emphasis; Advanced Mechanics (projectile motion); The Nature of Light (photoelectric effect)
  3. Exam 3 — The Nature of Light (emphasis): photoelectric effect, relativity, spectroscopy/diffraction — 21 marks plus extended response; Advanced Mechanics: projectile, orbital, banked circular motion — 18 marks; Electromagnetism: motor torque/back emf, transformers and AC transmission — 15 marks
  4. Exam 4 — From the Universe to the Atom (emphasis, 25 marks); Advanced Mechanics (18 marks); Electromagnetism (21 marks)
  5. Exam 5 — Advanced Mechanics (projectile motion, circular/banked motion, gravitation and orbits, energy) — emphasised; Electromagnetism (DC motors, parallel conductors, electromagnetic induction and transformers); The Nature of Light (photoelectric effect, special relativity)
  6. Exam 6 — Electromagnetism (33 marks, 41%) — motor effect, transformers, charged particles in fields, electromagnetic induction (Faraday/Lenz), AC generators; Advanced Mechanics (15 marks) — projectile motion, circular orbital motion and gravitation; The Nature of Light (14 marks) — special relativity, photoelectric effect graph analysis
  7. Exam 7 — Nature of Light (38/80 marks): photoelectric effect, special relativity, polarisation/diffraction, wave-particle duality, EMR models (Maxwell-Hertz-Planck-Einstein); Advanced Mechanics (12 marks): projectile motion, banked circular motion; Electromagnetism (14 marks): force between parallel conductors, ideal transformers and transmission losses
  8. Exam 8 — From the Universe to the Atom (emphasis, 41/80 marks); Advanced Mechanics — projectiles & circular motion; Electromagnetism — motor force & transformers
  9. Exam 9 — Advanced Mechanics (projectile, circular & banked-track, gravitation/Kepler) — emphasised weighting; Electromagnetism (transformers, parallel-conductor force, motor/Faraday-Lenz); The Nature of Light (photoelectric effect, EMR spectrum graph interpretation, special relativity)
  10. Exam 10 — Electromagnetism (motor effect, transformers, induction, charged particles) — heavily weighted; Advanced Mechanics (projectile, orbital, banked circular motion); The Nature of Light (photoelectric effect, wave-particle duality)
  11. Exam 11 — Nature of Light (photoelectric, spectroscopy, special relativity, wave-particle models) - ~41% weighting as the contextual emphasis; Calculation rigour: every numerical item shown formula -> substitution -> answer with units, recomputed and verified; Data/graph interpretation (photoelectric stopping-voltage vs frequency graph yielding Planck's constant and work function)
  12. Exam 12 — Advanced Mechanics (projectile, circular & orbital motion); Electromagnetism (motor effect, induction, transformers); The Nature of Light (EM spectrum, photoelectric effect, special relativity)
  13. Exam 13 — Advanced Mechanics (projectile, circular/banked, orbital & gravitation, synthesis) — 36/80; Electromagnetism (motor effect, transformers/induction, charged particles in fields) — 20/80; Nature of Light (photoelectric effect, quantum model) — 8/80
  14. Exam 14 — Electromagnetism (emphasis): motor effect, force between parallel conductors, transformers, charged particles in fields, EM induction & generators (30 marks); Advanced Mechanics: projectile motion, circular motion and satellite orbits (13 marks); The Nature of Light: special relativity (time dilation, length contraction) and the photoelectric effect with graphing (15 marks)
  15. Exam 15 — The Nature of Light (heaviest weighting — photoelectric effect, special relativity, blackbody radiation and spectra); Advanced Mechanics (projectile motion, circular/banked motion, orbital mechanics and Kepler's laws); Electromagnetism (charged particles in fields, transformers, electromagnetic induction, DC motors)
  16. Exam 16 — From the Universe to the Atom (heaviest weighting); Advanced Mechanics; Electromagnetism
  17. Exam 17 — Advanced Mechanics (projectile, circular/banked, gravitation, Kepler, 2D momentum) — emphasised, 34 marks; Electromagnetism (motor torque, back-emf, charged particle in B-field, transformer, Faraday/Lenz) — 22 marks; The Nature of Light (photoelectric effect, special relativity / time dilation) — 15 marks
  18. Exam 18 — Electromagnetism (emphasis, 31 marks): parallel-wire forces, transformers, charged particles in crossed/uniform fields, electromagnetic induction via Faraday's and Lenz's laws, and DC motor / back-EMF principles; Advanced Mechanics: projectile motion and circular/orbital satellite motion; The Nature of Light: photoelectric effect, special relativity (muon time dilation/length contraction) and wave-particle duality
  19. Exam 19 — The Nature of Light (special relativity, photoelectric effect, EM spectrum/Maxwell, blackbody radiation) — heaviest weighting per the exam's context flavour; Advanced Mechanics (projectile motion, uniform circular motion, gravitation and orbital mechanics); Electromagnetism (charged particles in fields, motor effect, Faraday/Lenz induction, ideal transformers)
  20. Exam 20 — From the Universe to the Atom (heavy emphasis: 40 of 80 marks); Calculation chains: formula to substitution to answer with units, every value recomputed; Photoelectric data/graph interpretation (Q25)

All 20 revision notes

  • Gravitational Fields and Orbital Mechanics
  • Gravitational Potential Energy and Escape Velocity
  • Projectile Motion: Independence of Components
  • Satellite Orbits: Speed, Period, and Energy
  • Uniform Circular Motion and Centripetal Force
  • AC Generators and Transformers
  • Electric Fields and Charged Particle Motion
  • Faraday's Law and Lenz's Law
  • Magnetic Force on Moving Charges and Current-Carrying Conductors
  • Torque on a Current Loop and the DC Motor
  • Nuclear Reactions: Fission, Fusion, and Binding Energy
  • Radioactive Decay and Half-Life Calculations
  • Stellar Nucleosynthesis and the Hertzsprung–Russell Diagram
  • The Bohr Model and Atomic Emission Spectra
  • de Broglie Wavelength and Wave-Particle Duality
  • Einstein's Postulates and Time Dilation
  • Length Contraction and Relativistic Mass–Energy
  • Maxwell's Prediction and the Electromagnetic Spectrum
  • The Photoelectric Effect and the Photon Model
  • Wave Behaviours of Light: Diffraction and Interference