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VCE · VCE Units 3 & 4

Physics

Fields, motion, waves and the quantum world — full exams with fully worked solutions and units.

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
9official past papers

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Sample revision note

Circular Motion: Horizontal, Vertical & Banked

1. Foundations of Uniform Circular Motion

An object in uniform circular motion (UCM) moves at constant speed but constantly changing direction. Because velocity is a vector, any change in direction — even at constant speed — constitutes acceleration. This acceleration always points toward the centre of the circle and is called centripetal acceleration.

The two core kinematic equations for UCM are:

  • Centripetal acceleration: a = v² / r, where v is the linear (tangential) speed in m s⁻¹ and r is the radius in m. Units of a: m s⁻².
  • Period and speed: v = 2πr / T, where T is the period (time for one complete revolution) in seconds. Frequency f = 1/T in Hz.
  • Combining: a = 4π²r / T² — useful when period rather than speed is given.

By Newton's second law, the net centripetal force required is:

Fnet = ma = mv² / r = 4π²mr / T²

This is not a new type of force — it is always provided by one or more real forces already present in the problem (tension, normal force, friction, gravity, or combinations thereof). In free-body diagrams, label the real forces only; centripetal force is the net result pointing inward.

Key sign convention: take the inward (centripetal) direction as positive when applying Newton's second law along the radial direction.

Worked Example 1. A 0.50 kg ball on a 1.2 m horizontal string makes 2.0 revolutions per second. Find (a) the period, (b) the linear speed, (c) the centripetal acceleration, and (d) the tension in the string (assume horizontal plane, ignore gravity for part d).

  • (a) Period: T = 1/f = 1/2.0 = 0.50 s
  • (b) Speed: v = 2π × 1.2 / 0.50 = 2π × 2.4 = 15.08... ≈ 15 m s⁻¹
  • (c) Centripetal acceleration: a = v²/r = (15.08)² / 1.2 = 227.4 / 1.2 = 190 m s⁻² (3 s.f.)
    Check via alternate formula: a = 4π² × 1.2 / (0.50)² = 4 × 9.870 × 1.2 / 0.25 = 47.37 / 0.25 = 189.5 ≈ 190 m s⁻² ✓
  • (d) Tension: Tstring = ma = 0.50 × 189.5 = 95 N

2. Horizontal Circular Motion — Conical Pendulum

A conical pendulum is a classic horizontal UCM problem. A mass m hangs on a string of length L that makes angle θ with the vertical, tracing a horizontal circle of radius r = L sin θ.

Two forces act on the mass: tension T along the string, and weight mg downward. Because the mass has no vertical acceleration, the vertical component of tension balances weight. The horizontal component of tension provides centripetal force.

  • Vertical: T cos θ = mg
  • Horizontal (radial, centripetal): T sin θ = mv² / r

Dividing the horizontal equation by the vertical:

tan θ = v² / (r × g)

Since r = L sin θ, substituting and solving for period:

T² = 4π² L cos θ / g → T = 2π √(L cos θ / g)

Note: as θ increases (faster spin), cos θ decreases, so the period decreases and the string sweeps higher — physically sensible.

Worked Example 2. A conical pendulum has a string of length L = 0.80 m making θ = 30° with the vertical. Mass = 0.20 kg, g = 9.8 m s⁻².

  • Radius: r = 0.80 × sin 30° = 0.80 × 0.500 = 0.40 m
  • Tension: From T cos 30° = mg: T = (0.20 × 9.8) / cos 30° = 1.96 / 0.8660 = 2.26 N
  • Speed: Tstring sin 30° = mv²/r → 2.26 × 0.500 = 0.20 × v² / 0.40 → 1.131 = 0.50 v² → v² = 2.262 → v = 1.50 m s⁻¹
  • Period: T = 2π√(0.80 × cos 30° / 9.8) = 2π√(0.80 × 0.8660 / 9.8) = 2π√(0.6928 / 9.8) = 2π√(0.07069) = 2π × 0.2659 = 1.67 s
    Verify via speed: T = 2πr/v = 2π × 0.40 / 1.504 = 2.513 / 1.504 = 1.67 s ✓
Sample exam question

During a long-jump take-off, an athlete leaves the board with a vertical velocity component of 4.9 m s⁻¹ and a horizontal velocity component of 8.0 m s⁻¹. Air resistance is negligible and g = 9.8 m s⁻². How long is the athlete in the air before landing back at take-off height?

  • A. 0.50 s
  • B. 1.0 s
  • C. 1.5 s
  • D. 2.0 s
Show the worked answer

Answer: B

Time to rise: t_up = v_y/g = 4.9/9.8 = 0.50 s. By symmetry total flight time = 2 × t_up = 2 × 0.50 = 1.0 s.

All 20 practice exams

  1. Exam 1 — Realistic VCE Section B weighting across all four areas (Motion 29, Fields & Electricity 33, Waves 19, Modern 29 = 110 marks); Every numerical answer recomputed in Python (formula -> substitution -> answer with units) and cross-checked for internal consistency; Long jump / athletics-stadium context flavour threaded through projectile, impulse, circular motion, induction, optics and photoelectric items
  2. Exam 2 — Motion: forces, projectile/circular motion, gravitation & orbits, momentum/impulse/energy (38 marks); Fields & electricity: transmission/transformers, EM induction, charges in fields, motor effect (36 marks); Waves & modern physics: special relativity, photoelectric effect, double-slit, de Broglie (36 marks)
  3. Exam 3 — Realistic VCE weighting across all four areas: Motion 25, Fields & Electricity 36, Waves 15, Modern Physics 34 (= 110); Particle-accelerator context woven through every question (photoinjector, beam optics, magnet cooling, grid supply, muon relativity, electron-diffraction probes); Every numeric answer recomputed in Python; one graph/data question (Q7) and explicit explain/justify items (Q4d, Q5c, Q6c, Q11c)
  4. Exam 4 — Realistic VCE Section B weighting across all four areas (Motion 34, Fields & Electricity 28, Waves 18, Modern 30 = 110 marks); Calculation chains shown as formula -> substitution -> answer with units, every numerical answer recomputed and verified in Python; At least one graph/data-interpretation question (Q5 photoelectric) and multiple explain/justify parts woven into an electricity-grid-transmission context
  5. Exam 5 — U3 AOS1 motion (Newton, circular, gravitation, momentum) - 38 marks; U3 AOS2 fields & electricity (motor effect, induction, transformers, charges in fields) - 36 marks; U4 AOS1 modern physics (relativity, photoelectric, de Broglie) - 28 marks + waves (double-slit) - 8 marks
  6. Exam 6 — Motion & mechanics dominate the paper (55/110): vertical & banked circular motion at the loop, energy conservation with friction, projectile launch, gravitation/orbits, a v-t graph data task, and momentum/impulse with a spring launcher.; Fields & electricity (19/110): a step-up transformer feeding the ride with a transmission-loss comparison, and an eddy-current magnetic braking fin via Faraday/Lenz and the motor effect.; Waves (17/110): standing waves in a closed warning-horn pipe plus beats, and a Young's double-slit laser light show including a 'find lambda' inversion and a qualitative change.
  7. Exam 7 — Charged particles in fields (qvB circular motion, acceleration through a pd, motor effect, induction) framed around MRI hardware; Modern physics depth: photoelectric graph analysis to extract Planck's constant and work function, de Broglie matter waves, and special relativity for a fast proton; Mechanics and AC electricity breadth: projectile/collision/gravitation plus transformer and transmission-loss reasoning, with explicit formula-substitution-units working
  8. Exam 8 — Realistic VCAA Section B weighting: Motion 28, Fields & Electricity 37, Waves 18, Modern Physics 27 (= 110 marks across 12 questions); Every numerical answer recomputed in Python (formula -> substitution -> answer with units) before output; Radio-astronomy context thread: dish actuators, observatory power, antennas, interferometer electrons, cosmic-ray muons; includes a graph/data question (Q10) and explain/justify items (Q4c, Q5c, Q7c, Q11d)
  9. Exam 9 — Realistic VCE weighting across all four content areas (motion, fields & electricity, waves, modern physics) with a unifying 'solar panels & photoelectric' context flavour; Every numerical answer verified by recomputation in Python; formula -> substitution -> answer with units shown in each sample solution; Includes a graph/data-interpretation question (Q5 photoelectric Ek-vs-f) and multiple explain/justify parts (Q4d, Q6c, Q7d, Q9c)
  10. Exam 10 — Fields & electricity (induction, motor effect, transformers/transmission) weighted heaviest — natural fit for the maglev context; Calculation rigour: every numerical answer recomputed (formula → substitution → answer with units) and verified; Spread across all four areas with a graph-interpretation item (Q13) and explain/justify items (Q3 Lenz, Q4, Q8, Q10)
  11. Exam 11 — Pendulum & energy context woven through mechanics (motion AOS dominant at 61 marks); Mandatory coverage: 1 graph/data-interpretation question (Q10 photoelectric) and 1 explain/justify question (Q8 transmission); Every numerical answer recomputed in Python before output; marks verified to sum to exactly 110
  12. Exam 12 — Motion: projectile, vertical circular motion, gravitation/orbits; Fields & electricity: power transmission/transformers, motor effect, EM induction; Waves & modern physics: standing waves, double-slit, photoelectric, relativity, de Broglie, sound/beats
  13. Exam 13 — Realistic VCE weighting across Motion (24), Fields & Electricity (39), Waves (18) and Modern Physics (29) — totalling exactly 110 marks; Authentic LIGO interferometry context threaded through every question (1064 nm Nd:YAG laser, suspended test-mass mirrors, seismic isolation, gravitational waves at c); Every numerical answer recomputed and verified; full worked solutions with formula, substitution and units; includes graph/data-interpretation (Q6, Q8, Q11) and explain/justify items (Q2d, Q4d, Q7d, Q8e, Q9d, Q10c)
  14. Exam 14 — Realistic VCE weighting across Motion, Fields & Electricity, Waves, and Modern Physics with the double-slit-with-lasers context woven through every question; Full formula-to-substitution-to-answer worked solutions with every numerical value independently recomputed and verified in Python; Data/graph interpretation (photoelectric Ek-vs-f plot) plus explicit explain/justify items on Lenz's law, transmission loss and relativity
  15. Exam 15 — motion & gravitation (Q1, Q11); fields & electricity (Q4, Q5, Q13); waves (Q8, Q9)
  16. Exam 16 — Electron microscope & matter waves context flavour threaded through every question (electron guns, magnetic lenses, electron diffraction, de Broglie wavelength resolution).; Full VCE Section B coverage: Motion (33), Fields & electricity (44), Waves (10), Modern physics (23) = 110 marks across 13 questions.; Every numerical answer recomputed in Python (formula -> substitution -> answer with units); includes a photoelectric graph-interpretation question and explain/justify parts.
  17. Exam 17 — Realistic VCE weighting across all four areas (Motion 28, Fields/Electricity 32, Waves 27, Modern 23 marks) with formula-substitution-answer calculations; At least one graph/data-interpretation question (Q10 photoelectric Ek-vs-f graph; Q9 diffraction data table) and explain/justify items (Q5 Lenz, Q9 diffraction, Q11 relativity reasoning); Every numerical answer recomputed in Python and verified; all per-part marks sum to question totals and questions sum to exactly 110
  18. Exam 18 — Realistic VCE weighting across all four study-design areas (motion/gravitation 29, fields & electricity 39, waves 20, modern 22 marks); Every numerical answer recomputed in Python (formula to substitution to answer with units) before output; Spacecraft gravitational-slingshot context threaded through all 11 questions, including data-interpretation and explain/justify items
  19. Exam 19 — Motion: projectile, circular (conical + vertical), Hooke/collisions, gravitation/orbits; Fields & electricity: motor effect/DC motor, transformers & transmission loss, EM induction; Waves & modern: standing waves, double-slit, photoelectric, relativity, de Broglie matter waves
  20. Exam 20 — Realistic VCE Section B weighting across all four areas: Motion ~27 marks (Q1, Q10, Q11), Fields & electricity ~26 (Q2, Q3, Q6), Waves ~24 (Q4, Q7, Q8), Modern physics ~33 (Q5, Q9, Q12 + Q4) — exactly 110 marks; Medical-imaging & EM-spectrum context flavour woven through every question (X-ray tube, magnetic beam steering, MRI bore field, gamma/UV photons, photocathode detector, hospital transformer feed, ultrasound-style standing waves, double-slit film QC, PET annihilation & relativistic isotope, imaging-relay satellite orbit, electron microscope de Broglie); Full exam-quality coverage: calculation items (formula -> substitution -> answer with units), one graph-plotting/gradient item (Q5) plus one data-table interpretation item (Q4), and explicit explain/justify parts (Q5d, Q7c, Q9c, Q12b); every numerical answer recomputed in Python before output

All 20 revision notes

  • Circular Motion: Horizontal, Vertical & Banked
  • Gravitation: Fields, Orbits & Kepler's Laws
  • Momentum, Impulse, Energy & Collisions
  • Newton's Laws of Motion & Forces
  • Projectile Motion
  • Charged Particles in Electric & Magnetic Fields
  • Electromagnetic Induction: Faraday's & Lenz's Laws
  • Generators, Transformers & Power Transmission
  • Gravitational, Electric & Magnetic Fields
  • The Motor Effect & DC Motors
  • Diffraction & the Wave Model of Light
  • Experimental Design, Uncertainty & Data Analysis
  • Interference: Young's Double-Slit Experiment
  • Mechanical Waves: Properties & Superposition
  • Special Relativity I: Postulates & Time Dilation
  • Special Relativity II: Length Contraction & Mass-Energy
  • Standing Waves, Resonance & Sound
  • The Electromagnetic Spectrum & Light
  • The Photoelectric Effect & Photons
  • Wave-Particle Duality & Matter Waves