Paper Clip Top or Sakai Top

It is possible to create a top out of a single piece of wire, for example a paper clip. Takao Sakai, professor of mechanical engineering at the Tohoku university in Japan, has proposed an ingeniously simple solution.

His top consists of a sector of a circle, from which two connecting spokes lead back to the main shaft, or rotating axis (see diagram).

The top will only work properly if the centre of gravity lies on the rotating axis; otherwise the top will not be stable. This will only be the case if tan(a/2)=1/2, with a being the angle between the spokes. It is a nice exercise for physics students to prove this. It follows that a = 53.13 degrees.

To build the top you need a pair of fine nosed pincers (pliers) and a metallic paper clip. While a was calculated assuming very sharp bends, in practice these are difficult to achieve; therefore you can compensate by making the angle a slightly smaller than 53 degrees. Using a regular paper clip, the height h and the radius of the circle r are about 1cm.

The Sakai top will run well even if the curvature of the circle is not perfect. With a well made top, you will see the circle and the shaft very clearly, while the rapidly revolving spokes will be invisible. When you spin the top with your fingers, the very small diamater of the wire will mean that the top revolves very fast, with speeds possible up to several thousand rpm. You can try to calculate roughly the speed of revolution depending on the diameter of the wire you have used, and the speed of your fingers as you spin the top, and then use a stroboscope to confirm your estimate.

The final trick - shown in the video - uses a tiny Neodymium magnet placed on the axis of the top, so as not to disturb the balance. The top will then be attracted to another metallic object, in this case another paper clip bent into a curved shape. The spinning top clings on to the curved shape and spins around its edge. This was originaly the basis of a Victorian toy.

Watch the video

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