The short answer
Name the real force playing the centripetal role in an unfamiliar system, then get the speed or the period out of a proportion rather than a formula.
Written and checked by GAMSAT tutors — not AI-generated.
Try the reasoning style
We treat forgetting as a failure — a lapse to be patched with reminders and records. Yet a mind that kept everything could not think; it would drown in the undifferentiated noise of every moment it had ever lived. To forget is not so much to lose information as to decide, mostly without our noticing, what was never worth keeping.
The author's argument relies most directly on which unstated assumption?
Pick an option to see how the tutor reasons to the answer — not just whether you were right.
Not quite — the answer is B.
Work backwards from the conclusion: a mind that ‘kept everything’ supposedly ‘could not think.’ That only follows if thinking means leaving most of experience out — so B is the premise the argument quietly rests on. A raises reliability, which the passage never weighs; C contradicts ‘mostly without our noticing’; D smuggles in a claim about intellect the passage never makes. The question rewards finding the hidden premise, not recalling a fact.
Section III hands you something unfamiliar going round and asks what changes. Velocity is a vector, so steady speed on a bend is still acceleration — v²/r inward, or 4π²r/T² from a period. Two moves answer nearly every such stem: name the real force doing the turning, then reason proportionally.
The two moves
Name the supplier
Newton demands an inward net force of mv²/r, and only a real interaction can supply it — string → tension; satellite → gravity; flat bend → friction; banked bend or centrifuge tube → the normal force. Centripetal is the job, not a force. No supplier, no circle: black ice sends a car straight on.
Then run the proportion
In orbit gravity takes the job: GMm/r² = mv²/r, so v = √(GM/r) — the orbiting mass cancels, and any option where orbital speed depends on it is dead. With v = 2πr/T this becomes T² = 4π²r³/(GM), a constant holding no r and no orbiting mass, so T²/r³ is identical for everything circling one central body.
mv²/r is never an extra arrow
A ball on a string has one real inward force, the tension; a second arrow labelled "centripetal force" counts it twice and every number after it is wrong. Draw the real forces, call inward positive, set their sum equal to mv²/r. Never an outward arrow either — that push in a turning car is your own inertia.
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| Moon | Mean orbital radius r (10⁵ km) | Period T (days) | T² / r³ (day² per (10⁵ km)³) |
|---|---|---|---|
| Io | 4.22 | 1.77 | 0.0417 |
| Europa | 6.71 | 3.55 | 0.0417 |
| Ganymede | 10.70 | 7.15 | 0.0417 |
| Callisto | 18.83 | 16.69 | 0.0417 |
Worked example
The International Space Station orbits every 93 minutes at 6,800 km from Earth's centre. How far from Earth's centre must a geostationary satellite sit to orbit once in 24 hours? You are given neither G nor Earth's mass.
Check yourself
A space telescope resolves two small moons in circular orbit around the same distant planet. Moon P orbits at a mean radius of 3.0 × 10⁵ km and takes 2.0 days per orbit. Moon Q orbits the same planet at a mean radius of 1.2 × 10⁶ km. Moon Q's orbital period is closest to:
Key takeaways
- Steady speed on a curve is still acceleration: v²/r inward, or 4π²r/T² from a period.
- Centripetal is a role, not a force — name the real supplier before you write anything.
- Real forces sum to mv²/r. Never draw mv²/r itself, and never draw an outward force.
- Same central mass? Take a ratio: double r and speed × 0.71, period × 2.8.
Practise this with real GAMSAT-style questions
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