A-Level Physics — 7) Circular Motion (IP-Friendly Guide)
Download printable cheat-sheet (CC-BY 4.0)14 Jul 2025, 00:00 Z
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
| 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 \(T\sin\theta = mv^2/r\) |
6 Mini-drill (3 min)
- Express 720° in radians.
Answer: \(4 \pi \space \text{rad}\). - Solve: A 0.40 kg mass whirls at 5.0 m.s(^{-1}) on a 0.60 m string. Find the tension.
\[ F = \frac{mv^2}{r} = \frac{0.40 \space \text{kg} \times 5.0^2 \space \text{m}^2 \text{s}^{-2}}{0.60 \space \text{m}} = 17 \space \text{N}. \] - 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
- 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.
9 Further reading
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.
