Observe the motion of the point, E, around the circle. The angle EOP is increasing at a constant rate. Describe the motion of point X.

## Summary/Background

- the distance OP is called the amplitude
- the velocity of x is written as \dot{x} and is greatest at O
- the velocity \dot{x} is zero at P and P'
- the acceleration \ddot{x} is zero at O
- the acceleration \ddot{x} is greatest at the end points P and P'.
- this motion is called simple harmonic motion (SHM)
- the angle \theta is increasing at a constant rate written as \dot{\theta} =\omega
- the equation \ddot{x} = -\omega^2 x describes the motion

## Software/Applets used on this page

Uses Cinderella interactive geometry

## Glossary

### acceleration

the rate of change of velocity with time. It is a vector quantity with magnitude and direction.

### amplitude

The maximum displacement from the x axis in either the positive or negative direction.

### circle

a conic curve with equation (x-a)²+(y-b)²=r²

### constant

a value in a formula or equation that cannot change.

### equation

A statement that two mathematical expressions are equal.

### simple harmonic motion

the motion of a particle moving in a straight line whose acceleration is always towards a fixed point on the line and is proportional to its distance from that point

### velocity

the rate of change of displacement. It is a vector quantity with magnitude and direction.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | M2 | Motion in a circle | Angular speed | - |

AQA AS Further Maths 2017 | Mechanics | Circular Motion | Angular Speed | - |

AQA AS/A2 Further Maths 2017 | Mechanics | Circular Motion | Angular Speed | - |

CCEA A-Level (NI) | M2 | Motion in a circle | Angular speed | - |

CIE A-Level (UK) | M2 | Motion in a circle | Angular speed | - |

Edexcel A-Level (UK - Pre-2017) | M3 | Motion in a circle | Angular speed | - |

Edexcel AS Further Maths 2017 | Further Mechanics 2 | Motion in a Circle | Angular Speed | - |

Edexcel AS/A2 Further Maths 2017 | Further Mechanics 2 | Motion in a Circle | Angular Speed | - |

OCR A-Level (UK - Pre-2017) | M2 | Motion in a circle | Angular speed | - |

OCR AS Further Maths 2017 | Mechanics | Motion in a Circle | Angular Speed | - |

OCR MEI A2 Further Maths 2017 | Mechanics B | Circular Motion | Angular Speed | - |

OCR-MEI A-Level (UK - Pre-2017) | M3 | Motion in a circle | Angular speed | - |

Universal (all site questions) | M | Motion in a circle | Angular speed | - |

WJEC A-Level (Wales) | M2 | Motion in a circle | Angular speed | - |