Wheel

The graphing window displays a circle of radius \(a\) in green, its center in purple, a radial line segment of length \(b\) in cyan, and a point (a "light") at the end of that radial line segment in yellow.

Set the wheel radius \(a\) and the radial setting \(b\) of the light using sliders at the bottom.

Animate the rolling wheel using the [>>] key, or control its position by grabbing the \(\theta\) slider, or by dragging the cursor over the graphing window with the mouse button depressed. During the animation the key changes to [||], and selecting it will stop the animation. At the end of the animation the key changes to [<<], which resets \(\theta\) to \(\theta = 0\). The value of \(\theta\), the angle of rotation, ranges from \(0\) to \(6\pi\) if \(a \lt 1\) and from \(0\) to the value of \(\theta\) at which the center has \(x\) coordinate \(6\pi\) if \(a \gt 1\).

Select the toggle [trace] to cause the light to leave a yellow trace and of the center of the wheel to leave a purple trace.

Select the toggle [velocity vector] to display the velocity vector in red.

Roll the cursor over the graphing window to create crosshairs and a readout of the cursor position.