The Physics of Tippe-Top Inversion

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The Physics of Tippe-Top Inversion: spinning things often have surprising physics! This video is from a segment of my talk I’ll be presenting tomorrow at PhysicsCon 2020 (Caltech’s Feynman Lecture Hall, Jan 4) where I will talk about flip over tops and other physics toys. In brief: friction with the surface provides a torque that acts on the existing angular momentum of the top to flip it over. The top will stay flipped until the spin rate slows down enough to where its center of mass pulls it back to the resting position. Inversion phase shown at 240fps- note the little hop the top takes as it goes on to its stem! 

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 

Tiny Tippe Top

Available from this shop in Germany: 
From experimentis-shop.de: BUY NOW Tiny Tippie-Top 

Educational Innovations has reasonably priced, regular sized, wood tippe-tops in their shop: 
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Tiny Tippe-Top: spinning things often have surprising physics! The smallest functioning version of the famous flip-over top I've ever seen. Friction with the mirror provides a torque that acts on the existing angular momentum of the top to flip it over. The top will stay flipped until the spin rate slows down enough to where its center of mass pulls it back to the resting position. 


Precision Tippe Top

Get a flip over tippe-top here:   

STEMcell Science Shop: BUY NOW Tippe-Tops 

Precision Tippe-Top: spinning things often have surprising physics! This aluminum version of the famous flip-over top works better than any I’ve seen. Friction with the desk surface provides a torque that acts on the existing angular momentum of the top to flip it over. The top will stay flipped until the spin rate slows down enough to where its center of mass pulls it back to the resting position.

Fruit Themed Tippe-Top

This quality wood toy available here: 
From eBay: BUY NOW Hape Spinning Top 

More flip tops here:
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Fruit Themed Tippe-Top: spinning things often have surprising physics! This colorful top by Hape not only flips over when spun, it also exhibits interesting behavior due to instabilities as it slows down- serious break dance moves! Friction with the mirror provides a torque that acts on the existing angular momentum of the top to flip it over.

 

Fine Wood Tippe-Top

Handmade flip over tops available here: 
From Art of Play: BUY NOW 
Flip Over Tops

See a selection of handmade hardwood tops here: 
From Etsy: Fine Wood Tippie Top 

Check out my short blog post on the history and physics of the Tippe-Top 

Fine Wood Tippe-Top: spinning things often have surprising physics! This lathe worked version of the famous flip-over top is made of ebony and wood from the pink ivory tree. Friction with the mirror provides a torque that acts on the existing angular momentum of the top to flip it over. The top will stay flipped until the spin rate slows down enough to where its center of mass pulls it back to the resting position. 


Mega Tippe-Top

Here is the mega tippe-top compared to typical tippe-tops on the market and a US quarter dollar:

Limited quantities available from the Spinning Top and Yo-Yo Museum of Burlington, Wisconsin 

Educational Innovations has reasonably priced wood tippe-tops in their shop: 
From Educational Innovations: BUY NOW Tippe-Tops 
From Amazon: BUY NOW Tippe-Tops 

Mega Tippe-Top: spinning things often have surprising physics. This giant version of the famous flip-over top must be launched with a string pull to give it enough rotational energy to make the flip. It is also placed on a concave mirror to keep it from wandering too far. Friction with the mirror provides a torque that acts on the existing angular momentum of the top to flip it over.