MathsNet: M - Motion in a circle - Illustration

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Awarding Bodies

Page ID: 2280

M | Motion in a circle | Angular speed | «Illustration»

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.

Please enable Java for an interactive construction (with Cinderella).

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

Cinderella

Uses Cinderella interactive geometry

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	-