Mg-3 The Cycloid
Published: Thursday 09 March 2006 - Updated: Wednesday 18 April 2007
Aim
To illustrate some of the unique properties of the cycloid.
Apparatus
Cycloid Board
Diagrams
Click on pictures to enlarge.
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Description
The Cycloid is the path of a point P(x,y) on the rim of a rolling wheel. where:
Two properties of the cycloid are:
1. The cycloid is the path of most rapid descent from A to B of a particle subject to gravity, initially at rest. Balls may be `raced' along the three paths to see which wins.
2. On a cycloid, the time of descent (from rest) from A to B is the same as from an arbitrary point C to B. Therefore, balls released simultaneously from A and C will collide in the middle at B.