We’ve all seen it. We’ve all felt it. And I’ll bet there isn’t anyone out there who can fog a mirror who hasn’t been confused by it. Whether it was a spinning bicycle tire in high school physics class, or something briefly covered in ground school, it’s still fascinating. Why the heck does a rotating mass respond to a force as if that force were acting a quarter-turn ahead of where it was actually applied? How can that be? Read on, and join the cognoscenti…
‘SEEING’ THE FORCE
Let’s do a little thought experiment. We’ll create a wheel, like the one here, spinning vertically and suspended in space. (We’re showing it here in somewhat of an oblique perspective to allow room to ‘write’ on one of its faces.) As you can see, it’s spinning with the top coming ‘out of the page’ and the bottom going ‘into the page.’ If the wheel actually existed, it would roll toward you when set down. Now we’ll apply a force to the top of the wheel, from the left — as in this first figure — and here comes the theoretical part. Imagine we can pick one small piece of this wheel, labeled ‘A’, and another at the other side, labeled ‘B.’ Particle A is moving downward, and B is going upward. Remembering Newton’s First Law, these particles ‘want’ to travel in their original direction — and in a straight line — as represented by the green arrows (or vectors).
Now imagine that the wheel is tilted 45 degrees over as a result of the force applied in the first figure. The result would look like this second illustration — provided the wheel was not spinning. Notice though that parcels A and B still have those vectors attached, and ‘want’ to move in their same original directions. (For the moment, we’re ignoring that.)
Now let’s carry this a bit further. We’ll honk that wheel around a full 90 degrees ‘nose down.’ What do we see? The vectors for our stubborn particles A and B are now pointing perpendicular to the wheel! If we let nature take its course — that is, let A and B go where they wanted to all along — the wheel would ‘yaw’ to the right…
…such that the point ‘B’ is now on top, the point ‘A’ is on the bottom and we’re looking at the wheel’s ‘back side.’ In other words, the original force has had the end result of acting 90 degrees ‘later’ along the wheel’s direction of rotation! (In actuality, particles A and B would be on the right and left sides of the wheel by now — not at the top and bottom — because this transition or ‘yaw’ doesn’t really have these ‘pretend’ intermediate stages … but you get the general idea.)
THE FINER POINTS
Every rotating object possesses two innate qualities:
- Rigidity in space, which can also be stated as resistance to motion.Example: This is the principle of the gyroscope, which allows us to use our attitude indicator to keep the shiny side up in IMC.
- The second is the property of ‘moment of inertia,’ which is the rotational analog to mass. A wheel has a moment of inertia, which comes from multiplying mass times the square of the spinning object’s length or diameter.Example: A spinning rod (such as a propeller) has a moment of inertia, but a bit less than that of a wheel of similar diameter. (Were its length the same as the diameter of our wheel, and if its weight were the same, it would have about two-thirds less energy.)
WHY IT MATTERS
Of what worldly use is all this? Well precession is what would save the day if you lost that vacuum driven attitude indicator. Precession is what makes your turn coordinator work! …but that’s a mind bender for another time. For now, you can enjoy basking in illumination and impressing your less well-read friends. as you explain that pushing the nose over very hard while turning the prop at high rpm will result in, of course, a negative-G pushover and petrified passengers — but also a healthy yaw to the left! (This is also what happens — to some extent — when a conventional gear airplane’s tailwheel lifts off the ground on the takeoff roll.) Think about it.