Re: How can a gyroscope seemingly defy gravity?

It is difficult to answer this question without a discussion about the vectorial forces on the spinning top. So, I'll answer this is two steps: the first, a physics answer, and the second part will be an attempt to qualitatively relate these concepts to everyday things (although, I admit that defying gravity is not an "everyday thing"...).

In the figure below left, w is the frequency of rotation of the gyroscope, g is the force of gravity, and L is the angular momentum vector, which for any rotating object is perpendicular to the rotation. In the left picture, the top is spinning vertically. When the top begins to tip, we have the figure at right. r is the radius vector from the "hinge" at the bottom tip of the gyroscope.

As you know, the figure at the left does not last for very long. As soon as it begins to tip (because of gravity), gravitational torque, denoted by the cross product of r and g, is induced. The direction of this torque is perpendicular to both r and g, and therefore causes a rotation about the vertical axis. This is denoted by dL/dt in the right figure, and is commonly called precession. Even if the gyroscope is horizontal (admittedly a difficult feat requiring a very nice pivot!), the rotation, combined with gravitational torque causes the precession. Angular momentum makes it all happen, and it's more convenient to think of this problem as a torque, rather than a force, balance problem. Fast rotation generally makes a top more stable.

All right, everyday things to think about, and I should make a disclaimer that the following examples are not exactly like the gyroscope, physics-wise. However, I hope they act as examples of how angular movement seems to "defy gravity". Lassos: spin it around and it stays over your head, rather than falling loose. Those amusement park rides where you're in a spinning room and the floor drops: in this case centripetal force keeps you pinned to the wall. Hula hoops...