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 | - |