TOYS, TRICKS, & TEASERS

By Donald Simanek

The Spinning Cylinder Illusion

This is a toy, a puzzle, and an illusion all in one, with only one moving part. No batteries are required. I like simplicity, especially when it produces puzzling complexity.

^» I’ve not been able to track down the origin of Here’s a sequence of photos showing the cylinder this homemade toy, but it isn’t very well known beginning to spin (Figure C), not quite settled down outside the community of physics teachers. It’s (Figure D), and finally spinning in one place with a kinetic illusion, one that depends on physical nearly constant angular speed (Figure E). These motion to make you see something that isn’t there. photos were taken with a digital camera, but they A familiar example of a kinetic illusion is the show approximately what appears to the eye. strobe effect sometimes seen in old movies, causing All these photos are taken from the same camera the spokes of a carriage wheel to seem to be turning position and distance, and reproduced at constant in the wrong direction. scale. Therefore lengths on the pictures may be In its simplest form, this toy consists of a hollow directly compared. Notice that a stable illusion cylinder of rigid plastic. The version in these photos showing 4 equally spaced dots occurs when the is 4cm long and 1cm in diameter, with 2mm wall cylinder rotates about its center, and both ends thickness. It was cut from a piece of polyethylene traverse the same circle, which has a diameter plastic tubing that happened to be lying on my equal to the length of the cylinder. workbench. Whatever tubing you use, be sure to The puzzling outcome is that when the cylinder choose a very straight piece. settles down to a uniform spin rate at a particular This material can be cut easily with a single-edged location on the table, you see only one color dot razor blade, scrap of board, and hammer. Use heavy (red, in this case), repeated N times, where N is gloves and goggles in case the razor blade breaks. the ratio of the cylinder’s length to its diameter. Or use a hacksaw, then smooth up the cut with fine The dot you see is the one at the end you pressed sandpaper. Cut the piece initially a bit long, then with your thumb to launch it. You don’t see any shorten it to optimum length by trial. I’ve made evidence of the dot at the other end (green, in this small ones in 2-, 3-, 4-, and 5cm lengths. I’ve also case). Launch the cylinder by pressing the green made them from the barrels of old ballpoint pens, dot end and then you see only the green dot, and and larger ones from PVC plumbing pipe. not the red one. Glue or paint a red dot near one end and a green How can we explain this unexpected behavior? dot at the other end, or use a felt-tip marker to Note that translational motion of the cylinder’s make distinctive symbols at the ends. center of mass stops just before stable dot patterns become visible. Note also that what we call the “stable motion” occurs when the ends of the cylinder trace a circle. When you think you’ve got it figured out, test your understanding by considering this follow-up question. If you spin this toy on a glass sheet, and someone looks up at it from below the glass, which colored dot would that observer see? A glass-topped coffee table is good for this experiment. What would be the optimum length-to-diameter

The Vanishing Dot Place the cylinder on a flat surface. It’s best to choose a surface that won’t dent or scratch, like a smooth, hard floor. Press down on 1 side of 1 end with your thumb, as shown in Figure B, until the cylinder slips away from your thumb and flies off spinning. It will settle down, revolving about its midpoint and at the same time spinning about its long axis (Figure A).

172 Make: Volume 16