I'd like to know who's really steering -- the contact patch or gyroscopic precession. When does one steering influence dominate over the other.
Normally the ball top goes straight so it seems that the contact patch has no influence, it can't make it steer.
I would say that in normal tops too, it is the gyroscopic precession which produces the steering, and not the contact patch.
Anyway, at very low speed, the ball top steers.
I believe that at very low speed the contact patch contributes to the steering.
But I try to explain better my thought about tops steering, (precessing):
I will call the sides of the flywheel with different names;
the front side, along the precession motion, is the "head", and the opposite side is the "tail".
The side towards the center of the circle of the precession is the "inner wing", and the opposite side is the "outer wing".
The inner wing is always the lowest part of the flywheel, the outer wing is always the highest part of the flywheel, and the head stays always at the same height of the tail.
The top steers, towards the right in this case, (blue arrow), because
the head is going upwards and the tail is going downwards.
This is not very intuitive.
Playing with a disc, (photos below), can help understanding.
Suppose that the circumference of the lower part of the disc represents the circle of the temporary contact points in a ball tip;
the flywheel is always parallel to this circumference, and the lowest part of the flywheel, (the "inner wing"), corresponds to the side of the tip which is temporarily in contact with the spinning surface.
If this imaginary top spins clockwise, the top goes towards the right, (photo below), driven by the ball tip, acting like a traction wheel.
The direction of the precession is tangent to the circumference at the contact point.
Now, the counterintuitive part;
while keeping the disc in contact with the ground at one side, try to rise the "head" and to drop the "tail", by the same distance.
What does it happen ?
Intuitively, one could think that the result of this action is that the disc will end in a position with the head in a higher position, and the tail in a lower position, but this is not what it happens.
What it happens is that the contact point has shifted by some degrees, so the direction towards which the tip is pushing the top has changed, towards the right in this case, so the top is steering.
The head and the tail too, (which stay always at 90 degrees from the "inner wing" and the contact point), become shifted some degrees later along the circumference;
the puzzling thing is that the head and the tail are still at the same height as before.
You can try this by yourself: take a disc and lean one side of it on a surface like in the photo;
then rise the "head" by maybe 10 mm, (for a disc with diameter about mm 100), and drop the "tail" by the same distance, 10 mm.
You will notice what I explained, the contact point becomes shifted by some degrees, and the "head" and the "tail", which have shifted too, are still at the same height as before.
So, the head going upwards and the tail going downwards, produce the steering motion.
The torque that makes the head to go upwards and the tail to go downwards comes from the weight of the top trying to topple down towards the inner wing side.
The gyroscopic effect translates this torque into motion with a 90 degrees delay, so the tail goes down and the head goes up, continuously, producing the precession motion.
The ball top has not the torque from gravity, so it doesn't steer, it doesn't precess, it goes straight.
Anyway, at very low speed, the gyroscopic effect doesn't work anymore, so a little revolution happens, the 90 degrees shift disappear, and the forces produce the motion in the same direction as they are applied.
This makes the top to change behaviour.
Normal spinning tops can't go so slow, because, as soon as the gyroscopic effect becomes too weak, they topple down.
But the ball top continues to spin even at quite low speed, when the gyroscopic effect has become very weak;
at this point the ball top starts to steer.
The translational deceleration of the top, makes the top to fall forwards, and, this torque, not shifted anymore by the gyroscopic effect, makes the head to go down and the tail to go upwards.
The rotational sliding friction too has a component that makes the head to go down and the tail to go upwards.
So the ball top at very low speed steers.
If the ball top has the flywheel slightly above the center of the ball, this introduces a tiny amount of precession, the ball top does not go exactly along a straight line, but it steers slightly, (to the right, if it spins clockwise). When this ball top has slowed down enough, and the gyroscopic effect is no more effective, the ball top
steers towards the opposite direction,(the left, if it spins clockwise).
The change of behaviour due to the gyroscopic effect not working anymore, makes possible for the ball tops to trace "S" shaped trajectories.
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Topic: Three experiments with gyroscopes (Read 9853 times)