A Level Circular Motion Hub
A Level Physics circular motion hub: radians, angular speed, and centripetal acceleration/force.
Learning goals
- Express angular displacement in radians and use s = rθ.
- Relate angular velocity, period, frequency and tangential speed using v = rω.
- Explain and apply centripetal acceleration and resultant-force relationships.
Circular motion connects rotational quantities to linear motion, then explains how a perpendicular inward resultant changes velocity direction even when speed is constant.
Core idea: “centripetal” means towards the centre. The inward resultant comes from real interactions; it is not an extra force type.
Minimum prerequisite route:
Common mark-loss errors: using degrees in radian equations, confusing constant speed with constant velocity, inventing a separate centripetal force, and changing the radial sign convention mid-solution.
After this hub: use the quick fluency warm-up for retrieval, then take the model-evidence form. Complete the Circular Motion Structured Set before treating the topic as strong or moving to mixed-topic transfer. Move to structured work when: you can build the radial force equation correctly from a new diagram without trial-and-error.
Lessons
Work through these lessons in order.
- Angular displacement in radians
- Angular velocity and tangential speed
- Centripetal acceleration and radial force models
- Radians & Angular Displacement
Express angular displacement in radians and use the arc-length relation s = rθ in A Level circular motion.
- Angular Speed, Period & Frequency
Use angular velocity, period, frequency and v = rω to connect rotation with tangential speed.
- Centripetal Acceleration & Resultant Force
Explain inward acceleration in uniform circular motion and apply a = v²/r = rω² and the corresponding resultant-force equations.
- Circular-Motion Force Models · Supporting
Build circular-motion force models from real interactions, a radial direction and Newton's second law.
Revision
Quick Reference
| Quantity | Formula | Unit |
|---|---|---|
| Angular velocity | ω = Δθ/(Δ t) = 2π/T | rad s⁻¹ |
| Linear velocity | v = rω | m s⁻¹ |
| Centripetal acceleration | a = rω² = v²/r | m s⁻² |
| Inward resultant force | ∑ Fᵢₙ = mrω² = mv²/r | N |
Angles must be in radians: 180° = π rad.
One force template
- Draw an FBD (real forces only).
- Mark the centre and choose inward as positive.
- Write the radial equation: ∑ Fᵢₙ = mv²/r (or mrω²).
- Use v = rω and ω = 2π/T as needed.
What You Must Memorise
- Radian: The angle subtended at the centre of a circle by an arc equal in length to the radius.
- Angular Velocity (ω): The rate of change of angular displacement.
- Centripetal Acceleration: Acceleration directed towards the centre of the circle (a = v²/r).
- Inward resultant force: ∑ Fᵢₙ = mv²/r = mrω². “Centripetal force” names this resultant; it is not a new interaction.
Top Exam Traps
- Centripetal Force: It is NOT a “real” force like Gravity or Tension. It is the Resultant Force (Fₙₑₜ) pointing to the centre. Never draw “Centripetal Force” on an FBD.
- Degrees vs Radians: Convert angular displacement to radians before using s = rθ; angular velocity in v = rω is measured in rad s⁻¹.
- Constant Speed ≠ Zero Acceleration: Direction changes, so velocity changes, so a ≠ 0.
- Radial Equation: Write ∑ F_(towards centre) = mv²/r with a clear inward direction.
Scope Boundary
The syllabus core is uniform circular-motion kinematics and the inward resultant. Vertical circles, conical pendulums and banked bends are useful transfer contexts: derive their equations from a fresh force model instead of memorising context-specific formulae. Circular orbits are developed in the next Gravitational Fields hub.
Practice
Quick fluency is a retrieval-rich warm-up for routing and formative feedback. Model-evidence practice checks force representations, limiting conditions, component models and real data. Paper 2 structured work is the independent production tier required before strong topic evidence.
Quick Fluency Warm-upModel-evidence PracticePaper 2 Structured ProductionA Level Physics Quiz HubStructured Practice HubNext hub: Gravitational Fields
Continue with the next resource in this course.
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027