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Thread: Close look at the gyro

  1. #1 Close look at the gyro 
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    Given a gyro, just a spinning disk: The faster a gyro spins, the truer it makes what we have to say about it. This one is horizontal more or less, spinning clockwise if you are looking down at it. No gimbals: it might be a rotary saw blade or a hula-hoop that we pretend is a disk.

    You apply tilting torque to the disk as though to pitch the closest point of its edge toward your toes. What happens?

    If a disk is coasting, we may assume that it is slowing down. If it is slowing down too slowly, you just won’t get to notice the effects we describe, that’s all. If spin is slowing down, its precession yaws down to your left The actual deflection will include a slight trace of pitch mixed in with predominant yaw because of a second order effect that we cannot totally ignore.

    If spin is speeding up its precession yaws down to the right.
    If spin is at constant speed it accumulates no net precession.


    Here is why to think so. As the disk spins:
    From any moment when steady torque pressure has been applied, the first 180 degrees of rotation henceforth will have accumulated an average downward deflection very near the extreme left edge of the disk. Dealing just with that downward yaw, we can see that the right-hand side of the disk will have flipped upward. Given a constant speed, the disk will find an equal amount of time in its second half-cycle being pushed back down along the portion of its edge that had been getting elevated during the first half-cycle. Hence, after a full 360 degrees of rotation, the disk would have been restored to its original attitude. Net yaw flip would be zero, hence no net precession.

    Given a falling disk speed, the consequentially extended period endured during the second half-rotation would result in a net downward yaw flip on the left-hand side. And so on for every full revolution of the disk.

    Given a rising disk speed, downward yaw-flip produced during the first half-cycle would never be quite compensated for by torque received during the second half cycle because that torque would always have been applied for a lesser duration than the for torque applied during previous half cycle. There would be a net downward yaw flip on the right-hand side.

    Most of our childhood studies of gyroscopic toys have naturally limited our experiences to declining spin velocities. Happily, we can grow out of such limitations. Twenty years ago, a colleague mentioned a weird effect produced by his massive table saw. As it finished a cut, it would zig from where it had been zagging to swing its cutting direction. For the first time, such a report makes sense: No doubt the saw would accelerate as the final cutting resistance diminished.

    Does that look right to anybody?


    Last edited by dalemiller; November 28th, 2011 at 07:26 PM. Reason: Knew that I would screw up left and right. Fixed
    "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense." --Buddha (563BC-483BC)
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  3. #2  
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    I apologise if I have misunderstood what you have written, but it seems to me that you are suggesting that a change in the rate of rotation of a spinning object gives rise to a change in the direction of the axis of rotation - is this what you are claiming?


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  4. #3  
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    Quote Originally Posted by JonG View Post
    I apologise if I have misunderstood what you have written, but it seems to me that you are suggesting that a change in the rate of rotation of a spinning object gives rise to a change in the direction of the axis of rotation - is this what you are claiming?
    Nope. I was examining the phenomenon that redirects torquing efforts from pitch to yaw. The direction of spin and its acceleration or deceleration seemed the most determining factors.Angular manipulation per se of the axis of rotation would be prompted by external thrust. Good gyroscopic action should prevail for various steady spin velocities, but precession occurs during the dwell of deceleration or acceleration. Let us note that a coasting top is just about always decelerating.
    Last edited by dalemiller; November 30th, 2011 at 10:24 PM. Reason: added spaces to separate words from each other
    "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense." --Buddha (563BC-483BC)
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