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.
