Tuesday, September 24, 2013

the Levitron

Few phenomena capture our attention as does the act of levitation— so counter to our expectations that gravity has cemented within our minds, we mostly find it on the magician’s stage. Yet here it is, the Levitron: spin stabilized magnetic levitation with no batteries or power source, manufactured by the cool gadget company Fascinations. The Levitron has two main components, a large donut shaped permanent magnet in the base, and a disk shaped magnet in the top itself, which are oriented such that the like poles of these two magnets repel. Hence, the pull of gravity is balanced by a magnetic repulsion, allowing the top to float for minutes at time.

Here is my short video on the operation of the Levitron:

To any physicist, an acute astonishment is felt upon a first encounter with this toy; it seems to violate Earnshaw’s Theorem which states that no configuration of non-moving permanent magnets can be in equilibrium. Typically if one tries to float a magnet above another, the loose magnet will quickly flip over and the opposite poles will come together with a snap. The key to achieving equilibrium (magnetic force v. gravity) with the Levitron is that the top is not stationary, it is spinning. Just as the conservation of angular momentum fixes the direction of a spinning gyroscope’s axis of rotation, the spinning top is similarly stabilized— but that’s not the complete story as other subtle physics principles play a role.

The actual act of getting the top to float is quite challenging. The strength of any permanent magnet is sensitive to temperature, so the repulsion force between the top and base can change from hour to hour, or from place to place if the Levitron is moved. The mass of the top must be adjusted precisely such that the push between the two magnets exactly balances with the pull of gravity— the smallest weight, an O-ring with a mass less than 1 gram, can make the difference of levitating or not.

In addition the axis of the top must tilt at a slight angle to become trapped, and the top must be spinning above a certain rate. Surprisingly, if the top is spinning too fast it will not float! These operating parameters of the Levitron, and many other surprising details, are described in this recommended paper by Martin Simon of UCLA. A thorough, high-level treatment of Levitron physics is presented in this seminal paper by Sir Michael Berry, where he shows that the magnetic trapping of a Levitron top is analogous to that used to trap single neutrons.

There are about five models of Levitron on the market. My favorite is the cherry wood model in the video, which allows a flight altitude of about 10 cm. No strings or illusions- just physics!

This physics toy is not currently in production, but some models are still available:

From eBay: Levitron Top

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