This is an old thread, but it's a topic I found interesting.
First patented in 1891 in Germany, the motion of this top was not properly understood until sixty years later. The inverting top was made famous as it attracted the attention of great minds like Niels Bohr, the Danish physicist who contributed to our understanding of the atom. It captured the world’s imagination throughout the 1950’s when it was mass distributed as a child’s toy. The inverted top is perplexing. When spun, it defies gravity, slowly turning upside down, becoming completely inverted. That’s exciting to watch! But this top performs an even stranger, more subtle trick. As the top inverts, the direction of rotation inverts. Spin the top right side up in a counterclockwise direction, and it will stabilize upside down spinning clockwise! Bohr wasn’t the first to ponder the motion of this curious top, the phenomenon was first discovered by watching children spinning local fruit in South America. Still, no one has more simply explained the counterintuitive motion than A. R. Del Campo. As the inverting top raises its center of mass against the force of gravity, the energy required to do the work must be obtained by a reduction of angular momentum. Therefore the top must spin slower after inversion. The reduction of angular momentum is only possible by an applied external torque. And only the force of friction is present to apply the torque.
The inverting top works because the center of mass is below the geometrical center of the sphere that forms the lower body of the top. Since the rotational axis must go through the center of mass, and the top must rotate about a point (Directly below the axis of symmetry) offset from the center of mass. As the top spins the force of friction acts against the offset, creating the torque which drives the stem down from the vertical and towards the ground. The stem will continue down from its initial vertical orientation until it becomes horizontal. Once there, the rotation about the stem fully stops. As the stem continues to be pulled downward the rotation through the stem starts up again, this time in the opposite direction, so that angular momentum maintains the same direction. Finally the top is drawn up on its stem by the torque generated by the force of friction. It has been transformed, spinning upside down and backwards, albeit a little be more slowly, as the rotational energy was consumed to raise the top upside down.
