Cycloid , Rotation

This applet helps you explore the cycloid which is the curve traced by a fixed point on the circumference of a circle as the circle rolls along a line in a plane.
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1-understand what is a cycloid.

2-find the coordinates of a point P on the circumference of a circle as it rolls along a line.

NOTE: you can change the radius of the circle (use the slider). You can use the auto mode or the step mode. If anything goes wrong just use the reset button.

1 - Use the system of axes (magenta) inside the circle to find the coordinates of point P (in this system) in terms of the radius of the circle and the angle that is changing.

2 - To find the coordinates of point P in the main system (black), add the coordinates of the center of the circle in the main system to the coordinates obtained in part 1 above.

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Updated: 27 November 2007 (A Dendane)