Suppose point A lies on a tire. At t = 0, A is on the ground. After the stopwatch starts, the tire starts turning to the right.
The path that point A takes as the wheel spins is called a cycloid.
The applet below shows two complete turns of such a wheel of variable radius.
(You can set this radius using the RADIUS slider.)
You can also adjust the speed at which the wheel turns with the SPEED slider.
Interact with the applet below for a few minutes. Then, answer the questions in your Calculus with Parametric Curves packet.