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VCE Physics exam: Thu 12 Nov, 9:00am — 33 days away
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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 ✓
- A. 0.50 s
- B. 1.0 s
- C. 1.5 s
- D. 2.0 s
Show the worked answer
Answer: B
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VCE Physics exam: Thu 12 Nov, 9:00am — 33 days away
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All 20 practice exams
- 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
- 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)
- 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)
- 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
- 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
- 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.
- 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
- 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)
- 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)
- 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)
- 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
- 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
- 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)
- 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
- Exam 15 — motion & gravitation (Q1, Q11); fields & electricity (Q4, Q5, Q13); waves (Q8, Q9)
- 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.
- 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
- 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
- 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
- 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
Common questions about VCE Physics
Which VCE Physics study design applies to my Year 12 exam?
The current accreditation covers Units 3 and 4 from 2024 through to 2027, so every exam from 2024 onwards is set against it. The 2017 to 2023 papers were written under the previous study design, and papers from 2016 and earlier belong to an older design again, when the subject was examined very differently.
Is VCE Physics still examined with two separate exams?
No. Since 2017 there has been a single end-of-year written examination covering all of Units 3 and 4. The two-exams-a-year format, with a mid-year paper and a November paper, belongs to the archived 2003 to 2016 study design, which is why those older papers are structured so differently from what you will sit.
Is Units 1 and 2 content on the VCE Physics exam?
The end-of-year examination assesses the Units 3 and 4 areas of study only, so Unit 1 and Unit 2 outcomes are school-assessed rather than examined. That said, Units 1 and 2 build the foundations — electric circuits, thermal physics and basic kinematics — that Units 3 and 4 assume you already have without re-teaching them.
Do you get a formula sheet in the VCE Physics exam?
Yes. VCAA supplies a formula sheet with the examination, alongside a separate answer sheet for the multiple-choice section, and publishes both with the examination specifications. Knowing what is on the sheet matters: the marks go to choosing the right relationship and rearranging it correctly, not to reciting formulas you could have looked up.
Does VCE Physics scale up or down?
Physics scales up. In the 2025 VTAC scaling report a raw study score of 30 scaled to 32. Scaling is recalculated every year, so this describes a past cohort rather than the year you are sitting.
What is included in the VCE Physics Mastery Pack?
Original practice exams with answer guides, worked questions, digital flashcards and revision notes for Physics. Complete revision notes are also available free. Official past papers are free external links, not material we sell. Preview the sample note, worked question and contents here. Paid resources unlock with a one-time purchase from $20, with access while the platform operates.
Where can I buy VCE Physics notes and practice exams?
You can buy the Physics Mastery Pack here as a one-time purchase: original practice exams with answer guides, revision notes, worked questions and flashcards. Printed study guides, trial-exam packs and student note marketplaces are other options, and official VCAA past papers are free — see the past-paper index for this subject.
Is the VCE Physics Mastery Pack a subscription?
No. It is a single payment per subject with no renewal, and access continues while the platform operates. You can preview a sample note, a worked question and the full contents before paying.
More detail: the study design explained · every official past paper by topic · how Physics scales · all 20 Physics revision notes · Physics practice exams with worked solutions