Motion in a circle at constant speed still has acceleration, because the direction keeps changing. That acceleration points at the centre and must be caused by a real force.
Syllabus points covered
- Understand the concept of angular speed and use v = rω
- Use the expressions for acceleration in a circle: v²/r and rω²
- Solve problems involving motion in a horizontal circle
- Solve problems involving motion in a vertical circle, including conditions for maintaining contact
Common mistakes
- Treating the centripetal force as an extra force in the diagram rather than the resultant of the real ones.
- Using v²/r with ω instead of v, or the reverse.
- In vertical circles, forgetting that speed changes and energy must be conserved.
- Missing the condition for a particle to leave the surface, where the normal reaction reaches zero.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questions
- Mark scheme
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Further Mathematics past papers