School of Physics Lecture Demonstration Manual

Mg-3 The Cycloid

Published: Thursday 09 March 2006 - Updated: Thursday 24 March 2011

Aim

To illustrate some of the unique properties of the cycloid.

Apparatus

Cycloid Board

Diagrams

Click on pictures to enlarge.

Cycoid Pic

Cycloid Diagram

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.

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