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”, yet it binds at least 12 marks across Papers 2, 3 and 4 every year. Nail radians, v=rω, a=rω2 and F=rmv2
early to free up mental bandwidth for gravitation, satellites and SHM later in the IP track.
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
A single sign slip in centripetal vs centrifugal language can cost an A-grader 3 marks, and those errors correlate strongly with first-term conceptual gaps.
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, not 180 deg.
WA tip: Always label the axis on your graph with radians to avoid a UMS penalty.
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 \( T \cos\theta = mg \) then \( T \sin\theta = \dfrac{mv^2}{r} \)
6 Mini-drill (3 min)
Express 720° in radians. Answer:4π rad.
Solve: A 0.40kg mass whirls at 5.0m⋅s−1 on a 0.60m string. Find the tension. F=rmv2=0.60m0.40kg×5.02m2⋅s−2=17N.
Explain why passengers feel “heavier” at the bottom of a Ferris-wheel arc. Hint: Reaction = mg+rmv2.
7 Bridging to Paper 4 practical
Plot v2 on the y-axis against r1 on the x-axis; the gradient gives rmv2 directly, letting you extract m if v is controlled. Always quote ± one standard error from the LINEST output.
8 Three WA timing rules
2 min per mark - Data-heavy Circular Motion items require extra calculator time.
Write the radial direction beside your FBD before summing forces.
Keep units visible; missing the “per-second-squared” costs one accuracy mark.
Comprehensive revision pack
9478 Section I, Topic 7 Syllabus outcomes at a glance
Outcome (a) - define angular displacement, velocity and acceleration in radians.
Outcome (b) - relate linear and angular speed/acceleration.
Outcome (c) - analyse centripetal force for objects moving in horizontal and vertical circles.
Outcome (e) - carry out experiments that verify centripetal relationships (Paper 4 link).
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
\( \omega = \dfrac{\Delta \theta}{\Delta t} \)
Angular acceleration
\( \alpha = \dfrac{\Delta \omega}{\Delta t} \)
Linear-angular link
\( v = r \omega, \quad a_t = r \alpha \)
Centripetal acceleration
\( a_c = r \omega^2 = \dfrac{v^2}{r} \)
Centripetal force
\( F_c = m a_c = m r \omega^2 = \dfrac{m v^2}{r} \)
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.
Worked example 2 - conical pendulum
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.
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.
