Circular motion looks deceptively “plug-and-chug”, but it underpins vertical-circle forces, banked tracks, and conical pendulums - and it feeds directly into gravitation, satellites and SHM later.
Key points
Nail radians, \\( v = r \omega \\), \\( a = r \omega^2 \\) and \\( F = \dfrac\{mv^2\}\{r\} \\) early to free up mental bandwidth for the harder integrations later in the IP track.
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1 Where this fits in the syllabus
2 Angular displacement in radians
Q: What does A-Level Physics: 7) Circular Motion Guide cover? A: From angular displacement to centripetal force, this guide unpacks Topic 7 of the 2026 H2 Physics syllabus for IP students and parents.
TL;DR Circular motion looks deceptively “plug-and-chug”, but it underpins vertical-circle forces, banked tracks, and conical pendulums - and it feeds directly into gravitation, satellites and SHM later. Nail radians, v=rω, a=rω2 and F=rmv2
early to free up mental bandwidth for the harder integrations later in the IP track.
Quick study map
If you only have...
Focus on...
1 second
The resultant force points toward the centre
10 seconds
Radians, angular speed, and centripetal acceleration
100 seconds
The first force-diagram and formula setup
10 minutes
Vertical circles, banked tracks, and conical pendulums
Concrete example: how to use this page
For a car turning a corner, do not invent an outward force. Draw the real force that points inward, then set it equal to (mv^2/r). The same habit works for strings, tracks, and satellites.
Cross-reference our free H2 Physics notes for adjoining gravitation/SHM chapters and downloadable drills so your revision plan follows the full Topic 7→Topic 9 arc. For the full topic map and paper weightings, see our H2 Physics Syllabus 2026-27 overview.
1 Where this fits in the syllabus
The SEAB 2026 H2 Physics syllabus positions Circular Motion as Topic 7 in Section I - Mechanics. IP schools typically teach it right after Dynamics so that normal-reaction questions in vertical circles feel like natural extensions.
1.1 Why parents should care
Sign slips in the radial direction (and mixing up centripetal vs “centrifugal” language) are common sources of lost method marks early on; fixing them early makes later gravitation/satellite/SHM work much smoother.
2 Angular displacement in radians
Radians measure “arc length per radius”, making every calculus derivative in later topics cleaner.
Quick check: Half a revolution = π rad (=180∘).
WA tip: Always label the axis on your graph in radians (not degrees) to avoid losing easy accuracy marks.
3 Angular velocity ω
Define:
ω=ΔtΔθ
with θ in radians and ω in s−1. The linear (tangential) velocity at radius r is
v=rω.
This falls straight out of “distance = rate × time” when the arc length s=rθ is divided by t.
4 Centripetal acceleration ac
Uniform circular motion means the speed is constant but the velocity changes direction, producing an inward acceleration
ac=rω2=rv2.
Direction: Always toward the geometric centre, perpendicular to v.
Intuitive cue: Rotate the velocity vector by 90° then scale it by rv.
5 Centripetal force Fc
Newton's Second Law packages the previous result into
Fc=mac=mrω2=rmv2.
The sharper the bend (small r) or the faster the motion (large v), the larger the required inward force.
5.1 Common exam archetypes
Scenario
Catch
Remedy
Car cresting a hill
Normal reaction can drop to zero
Equate weight to centripetal requirement
Roller coaster loop
Radial direction flips at the top
Draw FBD for each quadrant
Conical pendulum
Resolve tension into radial and vertical components
Use Tcosθ=mg then Tsinθ=rmv2
6 Mini-drill (3 min)
Express 720° in radians. Answer:4π rad.
Solve: A 0.40kg mass whirls at 5.0m⋅s−1 in a horizontal circle on a 0.60m string. Assume the tension provides the centripetal force. Find the tension. Answer:F=rmv2=0.600.40×5.02≈17N
Explain why passengers feel "heavier" at the bottom of a Ferris-wheel arc. Hint: Reaction = mg+rmv2.
7 Bridging to Paper 4 practical
To verify Fc=rmv2 experimentally, keep one variable fixed and plot a straight-line graph:
fixed r: plot Fc against v2 → gradient =m/r
fixed v: plot Fc against 1/r → gradient =mv2
Always quote ± one standard error from the LINEST output.
8 Three WA timing rules
Use syllabus pacing as a guide: Paper 2/3 average ~1.6 min/mark; Paper 4 ~3 min/mark.
Write the radial direction beside your FBD before summing forces.
Keep units visible; missing the “per-second-squared” costs one accuracy mark.
Need structured practice on Circular Motion? Our H2 Physics tuition programme covers this topic with weekly problem sets and Paper 4 practical drills.
Comprehensive revision pack
9478 Section II, Topic 7 Syllabus outcomes
Candidates should be able to:
(a) express angular displacement in radians.
(b) show an understanding of and use the concept of angular velocity.
(c) recall and use v=rω to solve problems.
(d) show an understanding of centripetal acceleration in the case of uniform motion in a circle, and qualitatively describe motion in a curved path (arc) as due to a resultant force that is both perpendicular to the motion and centripetal in direction.
(e) recall and use centripetal acceleration a=rω2, and a=rv2 to solve problems.
(f) recall and use F=mrω2, and F=rmv2
Concept map (in words)
Convert to radians, compute angular quantities, then translate back to linear variables when forces are required. Always identify the radial direction because the net inward force equals rmv2. Vertical situations demand additional energy/force checks at top and bottom. Banked motion and conical pendula link circular motion to equilibrium concepts from Topic 2.
Key relations
Quantity
Expression
Angular velocity
ω=ΔtΔθ
Angular acceleration
α=ΔtΔω
Linear-angular link
v=rω,at=rα
Centripetal acceleration
ac=rω2=rv2
Centripetal force
Fc=mac=mrω2=rmv2
Banking condition
tanθ=rgv2
Rotating frame weight
Apparent weight=mg±rmv2
Derivations & reasoning to master
Centripetal acceleration: derive ac=rv2 using vector subtraction or calculus (limit of chord angles).
Banked-track formula: resolve normal reaction components and solve for frictionless optimum.
Vertical circle tension: write Newton's 2nd law at top and bottom, showing how minimum speed arises from T≥0.
Energy + force blend: use energy conservation to find speed at various points, then plug into rmv2 for required force.
Worked example 1 - vertical loop
A 0.50kg cart enters a vertical loop of radius 1.8m at 12m⋅s−1 at the bottom. Find (a) its speed at the top (neglect friction), (b) the normal reaction at the top and bottom.
Sketch solution: use energy to determine the speed at the top v2=u2−4gR. Substitute into rmv2 to calculate reactions: top uses N+mg=rmv2, bottom uses N−mg=rmv2.
A 0.25kg bob moves in a horizontal circle of radius 0.65m with period 1.7s. Determine the string tension and the angle it makes with the vertical.
Approach: compute angular speed ω=T2π, then v=rω. Apply the radial equation Tsinθ=rmv2 and vertical equilibrium Tcosθ=mg to solve simultaneously.
ω=1.72π≈3.70s−1,v=0.65ω≈2.40m⋅s−1.
tanθ=rgv2≈0.904⇒θ≈42∘,T=cosθmg≈3.31N.
Practical & data tasks
Perform a whirling bung experiment; plot v2 vs radius and extract g from the gradient.
Use accelerometer data on a rotating turntable to compare measured radial acceleration with rv2.
Model banked curves using a coin on a wedge; measure limiting speed before slipping.
Common misconceptions & exam traps
Treating “centripetal force” as a new force; it is just the resultant toward the centre.
Using mg=rmv2 blindly without checking position in the vertical circle.
Mixing tangential and radial components when acceleration is not uniform.
Forgetting to convert revolutions per minute to radians per second.
Quick self-check quiz
Express 3 revolutions per second in rad⋅s−1. - 6πrad⋅s−1.
What provides the centripetal force for a satellite in circular orbit? - Gravitational attraction.
At the top of a vertical loop, what is the minimum speed to keep contact? - v=gr.
For a car on a banked track with frictionless surface, what relation links banking angle to speed? - tanθ=rgv2.
Why do occupants feel lighter at the top of a ferris wheel? - Normal reaction decreases because some of the centripetal requirement is supplied by weight.
Revision workflow
Redo three past-paper problems covering vertical circles, conical pendula and banked tracks.
Re-derive ac=rv2 weekly to keep the concept fresh.
Create a table comparing radial forces in different contexts (tension, weight, normal, electrostatic).
Practise sketching velocity and acceleration vectors for points around a circle without referencing notes.
Practice Quiz
Test yourself on the key concepts from this guide.
Parents: Book a 60-min Circular Motion clinic before WA 2 to bullet-proof free-body diagrams.
Students: Paste ac=rv2 on your water-bottle and test it on tomorrow's vertical-circle worksheet.
Last updated 14 Jul 2025. Next review when SEAB issues the 2027 draft syllabus.
