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Top Secret

This physics toy top is available here: 
From Educational Innovations: BUY NOW Mystery Spinning Top 

The amazing green magnetic viewing film is also available: 
From Educational Innovations: BUY NOW Magnetic Field Viewing Film 

Here is the 1974 patent showing the very simple circuit of this device. The spinning dipole (the top itself) induces a current in one of the coils, and this current is fed to the base of the transistor turning the electromagnet on when the top is near. 

"Top Secret": this top will stay spinning for more than a week- because it is actually a motor! The top is a dipole magnet (as revealed by Magneview film) and the base has an electromagnet that gives the dipole a push when the top comes near the center. An ingeniously simple circuit consisting of only a battery, a coil, and a transistor, is activated when the spinning magnet nears the coil turning on the electromagnet to give a boost to the spin of the magnetic top.

The Mirascope

I saw my first mirascope upon my initial visit to the Exploratorium when I was eight. I can still recall my astonishment. The exhibit entices you to pick up an illuminated spring, about four centimeters high and two centimeters in diameter— yet when you reached out to touch it, the spring is simply just not there! This was some serious physics magic! Sometimes mistaken for a hologram; this image is not produced using a LASER and the physics of interference and diffraction, but instead produced only by mirrors and reflection. 

The physics of the mirascope is fairly simple and yet the resulting 3D ghostly image seems simply magical. The mirascope consists of two parabolic mirrors facing each other in a clamshell fashion. The key to the design is that the focal point of each parabolic mirror sits at the vertex of the other, and a hole is made in the top mirror's vertex where the image is produced. To understand how reflection of light can create such an image, consider the special geometry of a parabola. A ray diagram illustrates how parallel rays of light that reflect off a parabolic curve will all meet at its focus (figure 1). This is the operating principle of satellite dishes or any parabolic reflector. It of course works in reverse: a light source located at the focus will reflect off the curve and leave the dish as parallel rays, a phenomena used by microwave communication antennas and searchlight reflectors. 

Placing two parabolic mirrors into the mirascope configuration (as seen in figure 2) puts the object to be viewed at one focus. The light leaving the object at this focal point reflects off the top mirror into parallel rays directed down. These rays then hit the bottom mirror which reflects them a second time to converge at the top focal point, creating the image at the top.

figure 2: Diagram included on the packaging  of the Opti-Gone Mirage

´╗┐´╗┐Amazingly, the mirascope was discovered by accident. Here’s a brief summary of the account (as described in these student conference proceedings by Adhya and Noé, page 367).  Sometime around 1969 a custodial worker at UC Santa Barbara was cleaning out a storage closet in the physics department. The closet contained a collection of carefully stacked WWII surplus searchlight reflectors— parabolic mirrors, each with a hole in its center for an arc lamp to protrude through. Serendipitously, these reflectors were stacked and stored in a clamshell fashion. The worker, Caliste Landry, found that there was dust “floating” in air at the top hole of one of the reflectors that “could not be cleaned”. He reported what he found to one of the young physics faculty members, Virgil Elings, who figured out the physics of the situation. Elings and Landry were awarded a patent two years later for their “Optical Display Device”. The rights of the patent were acquired by Opti-Gone International in 1977, and to this day Opti-Gone is the main seller of mirascopes which they market under the name “Mirage”. Elings went on to found Digital Instruments Inc. in the 1990s, where he attained many patents on scanning probe microscopy—  however, the mirascope patent, a physics toy, was his first!

Get one here! 
The larger version (Diameter = 9 in) as seen in the above video: 
From Educational Innovations: BUY NOW "Mirage" Mirascope 
From Amazon: BUY NOW "Mirage" Mirascope 

A smaller version (Diameter = 6 in) that works well too: ( plastic frog included ) 
From Educational Innovations: BUY NOW Small Mirascope 
From Amazon: BUY NOW Small Mirascope 

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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.

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 eBayLevitron Top 

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The tippe-top

Perhaps the most famous of physics toys: the tippe-top. Give this mushroom shaped top a spin on a semi-smooth surface and it will not only invert but change spin direction as it jumps onto its stem.

The dynamics of this top's behavior has been analyzed in numerous scientific papers, perhaps most famously in this paper by MIT physicist Richard Cohen published in 1974.  The inversion is primarily due to a torque applied to the top from slipping friction at the top's point of contact with the table. Torque, applied to existing angular momentum, leads to this dramatic inversion of the top's spin axis. The essence of Cohen's analysis is wonderfully captured in this short description and diagram by Frans Bilsen (caution- applied vector analysis involved).

No physicist can resist the allure of this physics toy, as this photo of two Nobel Laureates "demonstrating" the tippe-top will attest!

Figure: Wolfgang Pauli and Niels Bohr demonstrate a 'tippe top' toy at the inauguration of the new Institute of Physics at Lund, Sweden (1954) 
Photograph by Erik Gustafson, courtesy AIP Emilio Segre Visual Archives, Margrethe Bohr Collection 

Educational Innovations has reasonably priced wood tippe-tops in their shop: 

From Educational Innovations: BUY NOW Tippe-Tops 
From Amazon: BUY NOW Tippe-Tops 

The rattleback

Few toys have so wrought the attention of physicists as the rattleback. Attempts to pin down the physics behind the curious motion of this device are woven throughout the peer reviewed literature, and the sophistication of the math in some recent articles is on par with serious rocket science (as in this article by Lasse Franti of the University of Helsinki).

Rattlebacks all have a curious preference for a particular direction of spin− this one's "direction of stability" is counter-clockwise. Note that the reversal has two parts: First the clockwise spin is reduced as the kinetic energy transfers to a wobbling motion, then the energy transfers from this wobble to a spinning motion in the final direction.

The change of direction arises from a complex interplay of friction between the rattleback and the table top, a dance enabled by an instability due to the preferred axis of rotation not being aligned with the geometric axis of symmetry. This is quite like an unbalanced tire; vibrations will occur when spun. Early in the video one can see that the bottom of this kind of rattleback is somewhat propeller shaped. This asymmetry allows the preferred axis of rotation, related to the distribution of mass within the rattleback, to be different than the geometric axis. An alternative design has instead a symmetric bottom, but with added weights to offset the preferred rotation axis (of which I will show an example in a future post).

A shape so simple, yet behavior so complex that the most advanced theoretical techniques are needed to model it. A classic physics toy!

These acrylic versions work great and are inexpensive: 
From Educational Innovations: BUY NOW Rattlebacks 
From Amazon: BUY NOW Rattlebacks 
From eBay: BUY NOW Rattleback