Why should a gyroscope display this behavior? It seems totally nonsensical that the bicycle wheel's axle can hang in the air like that. If you think about what is actually happening to the different sections of the gyroscope as it rotates, however, you can see that this behavior is completely normal!
Let's look at two small sections of the gyroscope as it is rotating -- the top and the bottom, like this:
When the force is applied to the axle, the section at the top of the gyroscope will try to move to the left, and the section at the bottom of the gyroscope will try to move to the right, as shown. If the gyroscope is not spinning, then the wheel flops over, as shown in the video on the previous page. If the gyroscope is spinning, think about what happens to these two sections of the gyroscope: Newton's first law of motion states that a body in motion continues to move at a constant speed along a straight line unless acted upon by an unbalanced force. So the top point on the gyroscope is acted on by the force applied to the axle and begins to move toward the left. It continues trying to move leftward because of Newton's first law of motion, but the gyro's spinning rotates it, like this:
This effect is the cause of precession. The different sections of the gyroscope receive forces at one point but then rotate to new positions! When the section at the top of the gyro rotates 90 degrees to the side, it continues in its desire to move to the left. The same holds true for the section at the bottom -- it rotates 90 degrees to the side and it continues in its desire to move to the right. These forces rotate the wheel in the precession direction. As the identified points continue to rotate 90 more degrees, their original motions are cancelled. So the gyroscope's axle hangs in the air and precesses. When you look at it this way you can see that precession isn't mysterious at all -- it is totally in keeping with the laws of physics!