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The KE PE Track Model explains the curve traced by a point on the circumference of a circle as it rolls along a straight line, known as a cycloid.
There are two common types of cycloids based on the direction of rolling:
The equation of a cycloid for a circle of radius rr rolling along the x-axis is given by:
x(t)=r(t−sin(t))x(t) = r(t – sin(t)) y(t)=r(1−cos(t))y(t) = r(1 – cos(t))
where tt is a parameter representing time (or the angle the circle has rotated). This results in a series of arches that are characteristic of a cycloidal path.
Cycloidal paths are studied in various areas of physics and engineering, especially in designing smooth motion, such as in the catenary curves of bridges or the path of a rolling wheel.
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