For a beautiful demonstration of both magnetic force and gyroscopic motion, let's contemplate the Levitron. This novelty toy (which even now sits on my shelf waiting for a quick spin around the block) consists of a magnetic base upon which you spin a magnetic gyroscope. Both the bottom of the gyroscope and the top of the base contain magnetic north poles, and therefore they repel each other.
However, try as you might, you'll never be able to balance the magnet above the base without spinning the top. Why is this?
It's because even if you could get the magnetic and gravitational forces balanced for an instant, the whole thing is in a highly unstable equilibrium. Even the smallest disturbance is going to cause the gyroscope to partially flip over and fall to the base. Consider that somewhere towards the top of the gyro there must be a magnetic south pole (magnetic poles always occur in pairs). Once the gyroscope experiences any slight deviation from vertical it will experience a torque causing it to rotate and subsequently fall. In fact, according to Earnshaw's Theorem, there is no way to maintain a stable equilibrium for any arrangement of fixed magnets or static electrical charges.
But as we can see, hope is not lost. We can and will levitate our magnetic gyroscope. All we need to do is spin it, thus giving it an angular momentum. An object with a large amount of angular momentum becomes very difficult to move off of its spin axis. Have you ever considered why riding very slowly on a bicycle is so hard, but as you speed up it becomes so much more stable? The faster the tires spin, the more angular momentum they have and the more stable they are. They strongly resist any attempts to change their orientation. The same is true for any gyroscope. The result is that a torque applied to a gyroscope by gravity, rather than pulling it to the ground, will cause it to wobble in a circle about the spin axis. This wobbling is called precession. After a while (almost three minutes in the video!) the rotation rate and the angular momentum decrease sufficiently (as a result of air resistance) for the gyroscope to crash back down to Earth*.
All this being said, it is a bit tricky to get the Levitron to work just right. It's stable only for a narrow range of heights, its stability is affected by changes in temperature, and you often have to adjust the weight of the gyroscope with little washers to get it to balance. However, once you get the thing fine-tuned, once you get a solid two- or three-minute levitation going, you'll be mesmerized!
*It may interest you to know that our rotating home, planet Earth, also precesses about its spin axis, due to gravitational torques exerted by the Sun and Moon. The time for one complete precession of planet Earth is about 26,000 years.
Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.