Note: To get the most out of this activity, don't read this section until you've done some experiments yourself!
When you launch the cylinder, it spins around its long axis and rotates around a line perpendicular to this axis. As it rotates about its center, the cylinder forms a blurry circle on the table top. As the cylinder spins, the top of one end moves in the same direction as the end that is rotating, while the top of the other end moves opposite the rotation. The arrows in the diagram below, showing the pipe as seen from above, illustrate these relationships.
The two arrows within the cylinder show how it spins. The two arrows outside the cylinder show how it rotates. On the right end, the two motions cancel each other, and when the mark on the spinning cylinder is at the top, it actually stops momentarily (see the Going Further section below for the mathematical explanation). On the left end, the two motions add together, and when the mark on the spinning cylinder comes to the top, it moves twice as fast as it would with either motion alone (again, see the Going Further section below for the mathematical explanation).
Human eyes can see the stopped mark easily, while the extra-fast moving mark is a blur. Thus, only the mark on one end is visible. Since we see three marks around the blurred circle, we know that the cylinder is making three spins for every rotation (see the Going Further section below for the mathematical explanation). Cylinders that are cut so that their length is four diameters have a stable square with four markings. Those cut to two diameters create a stable pattern of two marks.
At first, using the cylinder that is three diameters long, the marks on one end appear but they do not form a stable pattern. After a few seconds, however, the marks settle into a stable triangular pattern which persists until the cylinder slows to a stop. To understand this behavior, notice that the cylinder spins and rotates with one end on the table and one end in the air. The cylinder makes a stable pattern when the end touching the table rolls without slipping. Usually the cylinder is launched so that it is spinning faster than it is rotating. This means that the end touching the table rubs against the table, dissipating energy and slowing down until it reaches a speed where it rolls without slipping. This is why the pattern is not stable at first, but then stabilizes.