Marcus' Puzzles Games Pages

Waggling Wood = Celtic Stone

If you spin the waggler clockwise on a table, after a while it will start to waggle, slow down, stop and finally reverse its spinning direction. Most people and every physicist is surprised by this phenomenon, since it seems to violate angular momentum conservation. There are several publications on this phenomenon, which was probably first discovered by the Celts when spinning pebbles of certain shapes. I found all published explanations unsatisfactory. A rigorous explanation should start with the rigid body equations of motion, possibly simplifying them while strictly respecting rotational symmetry and then showing that the spinning direction reverses while/although angular momentum of the closed system waggler+table is conserved. Energy is conserved by transferring it to and from angular momentum to waggling. The intuitive explanation is that the rotation axis is unstable and that angular momentum is transferred to the table by a non-central contact point, but the intuitive explanation alone is insufficient, since intuitively one can "explain" everyting (independent of whether true or wrong). Together with Andreas Blumhofer I spent some time deriving such a rigorous explanation but with limited success. We also tried tracking the waggler with a stereo vision system and comparing its motion with the numerical simulations, but the time-resolution was insufficient. We intended to build a larger (slower) waggler, but severity of life and the lack of time caught up with us.

Levitron

Two magnetic north poles repel each other, but trying to make one magnet levitate freely above another is not as easy as it may seem, since the levitating magnet flips over and is attracted. Gyroscopic forces can be used to stabilize the orientation of the magnet. The Levitron consists of magnets in the base with north side up and a magnetic gyroscope with north side down. If you spin it in a certain height above the base in the air it will levitate for several minutes. Since the air is the only friction, it would levitate forever in a vacuum chamber. The Levitron contains no battery or other source of energy!

Gyroscope

Just a gyroscope which can be spinned by unrolling a string.

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