A-Level Physics: Circular Motion Guide

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, \(v = r \omega\), \(a = r \omega^2\) and \(F = mv^2/r\) 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 = \(\pi\) rad, not 180 deg.
• WA tip: Always label the axis on your graph with radians to avoid a UMS penalty.

3 Angular velocity \(\omega\)

Define
\[ \omega = \frac{\Delta \theta}{\Delta t} \]
with \(\theta\) in radians and \(\omega\) in \(\text{s}^{-1}\). The linear (tangential) velocity at radius \(r\) is

\[ v = r\omega. \]

This falls straight out of “distance = rate x time” when the arc length \(s = r \theta\) is divided by \(t\).

4 Centripetal acceleration \(a_c\)

Uniform circular motion means the speed is constant but the velocity changes direction, producing an inward acceleration

\[ a_c = r\omega^2 = \frac{v^2}{r}. \]

Direction: Always toward the geometric centre, perpendicular to \(v\).

Intuitive cue: Rotate the velocity vector by 90° then scale it by \(v/r\).

5 Centripetal force \(F_c\)

Newton 's Second Law packages the previous result into

\[ F_c = ma_c = mr\omega^2 = \frac{mv^2}{r}. \]

The sharper the bend (small \(r\)) or the faster the motion (large \(v\)), the larger the required inward force.

5.1 Common exam archetypes

6 Mini-drill (3 min)

1. Express 720° in radians.
   Answer: \(4 \pi \space \text{rad}\).
2. Solve: A 0.40 kg mass whirls at 5.0 m.s(^{-1}) on a 0.60 m string. Find the tension.
   \[ F = \frac{mv^2}{r} = \frac{0.40 \space \text{kg} \times 5.0^2 \space \text{m}^2 \text{s}^{-2}}{0.60 \space \text{m}} = 17 \space \text{N}. \]
3. Explain why passengers feel “heavier” at the bottom of a Ferris-wheel arc.
   Hint: Reaction = \(mg + mv^2/r\).

7 Bridging to Paper 4 practical

Plot \(v^2\) on the y-axis against \(1/r\) on the x-axis; the gradient gives \(mv^2/r\) directly, letting you extract \(m\) if \(v\) is controlled. Always quote \(\pm\) one standard error from the LINEST output.

8 Three WA timing rules

1. 2 min per mark — Data-heavy Circular Motion items require extra calculator time.
2. Write the radial direction beside your FBD before summing forces.
3. Keep units visible; missing the “per-second-squared” costs one accuracy mark.

9 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Lumen Learning — Centripetal Acceleration
• Wikipedia — Angular Velocity
• IOP Spark — Proof of F = mv^2/r
• OpenStax — Uniform Circular Motion
• Lumen Learning — Centripetal Force
• Save My Exams — Radians & Angular Displacement
• Physics SE — Intuition for a = v^2/r
• YouTube — Derivation of v = rω
• Reddit — Why Radians Rule

10 Call-to-action

Parents: Book a 60-min Circular Motion clinic before WA 2 to bullet-proof free-body diagrams.
Students: Paste \(a_c = v^2/r\) 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.