The Button Spinner.

No physicist is likely to receive a Nobel prize for solving a problem in classical physics. Students assume there are no problems remaining in classical physics. They diligently learn quantum mechanics, relativity, string theory, etc. yet some would be unable to analyze the physics of a simple children's toy. But recent history has a few examples where classical mechanics mysteries have finally been resolved. Bicycle stability, baseball and golfball spin, the boomerang, the tippy-top and the rattleback have all now been dealt with. What remains?

There's a little toy common in my childhood, less often seen today, for it costs nearly nothing and can't be found in "Toys R Us". It requires no batteries, and isn't electronic, so a kid wouldn't ask for one if it were there. It is the classic button spinner. A simple plastic coat button and some stout string are all you need. to make one If you've never seen one, here's a U-Tube video. Thread spinner, the button-thread toy . This toy is old. In some cultures it is called the khua or diable, and is sometimes used in sorcery.

Actually, versions of this can be found in toy stores. They have been over-engineered with internal batteries powering LED lights. Toymakers have gimmicked up spinning tops and even the simple yo-yo in the same way. But the lights add nothing to the beauty of the physics in these classic toys.

The button spinner. ©Bob Friedhofffer.

It is a nice physics demo, illustrating conversion of work to energy and potential to kinetic energy and vice versa. Not much mystery there. You should make and use one to experience the tactile feel of it and master the most effective way to make it work. With a little practice you will anticipate when the string is fully wound and relax the tension to let it unwind, then anticpate when to increase the tension again, never allowing the string to go slack. It feels as if you are stretching a steel spring. Hands-on physics at its best.

Buttons at lest 2 inches in diameter are best. Some buttons don't work well at all. Their size, weight and hole spacing all affect performance. Why and how?

One mystery is seldom mentioned. Initially the spinner string is held loosely between your hands. Then you swing the button in a circle and the string winds up. What is the physics involved in this initial winding? What torque gets the button rotating during wind-up to twist the string and what are the dynamics of this process?

Experiment.

One correspondent told me that when he was young and soda bottles had crimp bottle tops, kids would flatten the tops with a hammer, punch two holes with a hammer and nail, and make little spinning "buzz saws". Then they would have a contest to see who first could succeed in sawing through the string of his opponent. In those days string was always available for kids' projects. Mothers saved the string from packages wrapped at the store (we called it "store string"), or from packages sent in the mail. They saved the brown paper wrapping as well. Children used it to fashion protective textbook covers.

Discussion.

I have a 4.5 inch soft plastic disk from a pudding container. Two holes are 1 cm apart for the strings. The string loop is about two feet long. When the strings are loose (hanging in a V), and the disk is swung as a pendulum, it doesn't seem to rotate at all. Draw an arrow on it, and the arrow points the same direction throughout many swings. But do a quick circular hand motion to initiate a flip, and after just one flip, the strings have wrapped just once.

Hanging in a V, the strings are unlikely to have exactly the same tension, and may even be one above the other. This initial small asymmetry means that when the flip occurs, the hole with the greater tension string segment moves through a smaller radius than the other one and the torques of the segments are unequal. The two string segments therefore exert a net torque on the disk even if they are the same tension, or nearly so.

In fact, even if the strings were at the same radius at the bottom of the flip, after 90° they would (with no rotation of the disk) have different radii during the larger circular motion, and therefore would be exerting a differenetial torque on the disk. The rotation and revolution quickly become phase locked. It would be near impossible to make the system so perfect as to avoid this outcome.

But why isn't this rotation of the disk about its own axis seen when it is swinging as a pendulum? Well, it does rotate a bit, but its own rotational inertia and its slow speed ensure that it doesn't rotate far before reversing direction on the next half swing. When flipped more forcefully around an entire circle it does manage to rotate 180 degrees, and continues to do so in subsequent revolutions.

Many thanks to John C. Denker for helpful discussions and insights about this puzzle.