# 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.

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.

__TUTORIAL____objectives:__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.

Calculus Questions - Geometry Tutorials - Precalculus Applets - Applied Math - Precalculus Questions and Problems -

Equations, Systems and Inequalities - Geometry Calculators - Math Software - Elementary Statistics -

Updated: 27 November 2007 (A Dendane)