Good question... and I agree that when you first learn about gyroscopes, things like cross-products and "right-hand-rule" can leave you without a good feel for why the thing works the way it does. And the way it acts is so cool that it really makes you want to understand why!
It might be nice to try to visualize the causes of precessuion directly in terms of forces, rather than using torques. In simple classical mechanics, there are only 3 basic rules:
(forces between two objects are equal and opposite, so momentum is conserved)
3. forces between two point-like objects are along the line between them (this gives conservation of angular momentum)
Everything else (like cross-products, right-hand-rule, torque etc etc) is formalism and definitions that helps with complicated problems. However, as the discussion below shows, trying to describe problems like this without using angular momentum/torque language is not easy!
In what follows, we use the second two properties in the background, when we assume that no object can twist itself.
First, I strongly encourage you to visualize the situation in great detail. It may take some time/effort/struggle to do this, but it could help you get a better understanding.
Imagine that youíre drinking coffee and are holding your mug in your right hand. When you tilt the mug toward you to take a drink, the rim changes from a flat circle to a tilted circle. Now imagine that for some reason, thereís an incredibly fast ant who is racing around and around (counter-clockwise) along the rim of the mug as youíre tipping it toward you. When he passes over your right hand, heís on an uphill section, but since youíre continuing to tip the mug as he runs, youíre making the hill steeper and steeper for him. The key is not that itís an uphill, but that youíre changing the slope of the hill as he moves along it. Although it would be too small a force for you to notice in this case, you actually have to give a little bit of upward force to keep pushing him onto this new direction (i.e. along a steeper path). Later in his trip, heíll be on a downhill section of rim opposite to your hand, and your tipping the mug toward you is making that section a steeper and steeper downhill. So, to keep the mug going straight toward you, youíll need to apply a little force to accelerate his mass downwards (i.e. a downward force on the left side of the mug). So, no matter where he is, youíre never letting him go straight uphill or straight downhill. It might be helpful here to really visualize that as long as you keep tipping the mug as he runs, he is not traveling
straight uphill or straight downhill.
To summarize, when he was near your hand, you had to keep pushing him up to keep him on the ever-changing course, and when he was on the side away from your hand, you had to keep yanking him down as you made it a steeper and steeper downhill. If there were two ants racing around (staying on opposite sides), youíd need to apply a "twist" - up on the right side and down on the left to keep the mug side-to-side
level. Thatís all there is to it. And by the way, it doesnít have anything to do with gravity; youíd still have to apply this force to keep changing his direction even if there was no gravity.
This idea of having to apply a force to change somethingís direction is very common. For example, if youíre in a car, youíll feel an upward "push" from the car as you go from a flat road to an uphill. And this push only happens while the steepness is changing... because a change on your path away from a straight line is an acceleration.
So, getting back to the spinning wheel (or gyroscope if you want to be fancy) you just need to realize that a wheel has mass all along the circle. While youíre twisting it, youíre forcing all the pieces of the wheel to constantly change direction, and so you need that crosswise twist to do that.
If you really try hard to visualize it, you can convince yourself that if you tip a spinning (counter-clockwise) wheel toward six-oclock, itíll try to tip toward three-oclock (i.e. youíd have to push toward nine-oclock to keep it flat). And, of course, thereís nothing magic about "six-oclock"; no matter what way you push, itíll try to twist 1/4-turn ahead. The term for this is "precessing." Note that the direction the wheel is spinning defines which way is "ahead" here; if itís spinning clockwise instead, then it'll push to 9-oclock when you tip toward 6'oclock. So, a spinning top that isnít perfectly vertical wonít just fall over. Instead, as gravity pulls it over, it will just
"precess" forward (this is why the spindle starts tracing out a big circle).
A bike works the same way. As long as the wheels are spinning, you can create a force to twist the wheels bottom-to-top (i.e. the twist that keeps you upright) by twisting them left-to-right (i.e. the twist that you can put on the front wheel by turning the handlebars).
That explanation got a little longer than I planned, but I hope that if you try again to think about this (and also think about it in your own way) that it will make sense. Itís great that you want to understand it so that it really makes sense... rather than just going along with an explanation that wasnít clear to you.
(republished on 07/13/06)