A spinning rod with a mark near one end is set rotating and spinning at the same time. Amidst the blur of the spinning cylinder, the mark appears three times, forming a stationary triangle.
A few feet of 3/4- inch (outside diameter) schedule 40 PVC tubing
A hacksaw or tube cutter
Colored pens (nonpermanent)
A smooth surface such as a table top
A transparent surface (optional)
Cut the tubing to three times its diameter in length (err on the long side; this experiment will still work with tubes up to 3.15 diameters long.)
Mark an "X" on the side of one end of the rod and an "O" on the other.
After the first experiment, you will need a few more pieces of tubing. Cut them so that you have a set of tubes with lengths that are two, three, four, and five times their diameters.
Place your finger on the "X," push your finger down as you pull it toward you. This will make it spin and rotate at the same time. The cylinder will spin and rotate making a blurred circle in which three X's can be seen.
Notice that the spinning cylinder stabilizes so that the X appears at the vertices of a triangle. Notice the O does not appear.
Next place your finger on the O and spin the rod.
Make several markings on one end.
Look at the spinning rod from underneath through a transparent table.
Look at the spinning rod in sunlight (which does not strobe on and off like fluorescent lights.)
Look at the spinning rod with a stroboscope. A hand made stroboscope in which slits are cut into the edges of a spinning disk will work just fine. (See the stroboscope activity.)
Draw a line down the side of the cylinder make one half of the line red and the other half blue.
Try cylinders of different lengths, notice the different stable patterns.
Notice that the center of the spinning cylinder is above the table, the cylinder rotates with one end in contact with the table surface.
Don't read this section below until you have done some experiments yourself.
When you launch the rod it spins about its long axis and rotates about a line perpendicular to this axis.
As it rotates about its center, the rod forms a blurry circle on the table top. As the rod spins, the top of one end moves in the same direction as the end is rotating while the top of the other end moves opposite the rotation.
The arrows on the cylinder show how it move, the entire top is moving down.
The arrows off of the cylinder show how it rotates.
On the right end the two motions cancel, and the top center comes momentarily to rest, on the left end they add.
The marking on the end that is moving opposite to the rotation slows down, for each pattern of marks, for example the triangular pattern, there is one place on the cylinder where the mark will come briefly to a complete stop. The marking on the other end is going doubly fast. Human eyes can see the stopped marking easily while the extra-fast moving marking is a blur. Thus only the markings on one end are visible.
Since we see 3 markings around the blurred circle we know that the cylinder is making 3 spins for every rotation. Cylinders that are cut so that there length is four diameters have a stable square with 4 markings, those cut to 2 diameters create a stable pattern of 2 marks.
At first with the tube that is 3 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. Notice also that the cylinder spins and rotates with one end in the air.
The key to understanding the behavior of the cylinder is to realize that:
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 the end of the cylinder rolls without slipping. This is why the pattern is not stable at first, but then stabilizes.
The circumference of the circle that the end moves
through as it goes around its blurry circle is pi times the
length of the cylinder or pi times three diameters of the