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Counter-torque in the gyroscope to oppose the torque

  1. Jun 15, 2010 #1
    https://www.youtube.com/watch?v=<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/cquvA_IpEsA&hl=en_US&fs=1&"></param><param [Broken] name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/cquvA_IpEsA&hl=en_US&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>

    I'm confused with what is causing the counter-torque in the gyroscope to oppose the torque by gravity. Is the force by the top a reaction force? It says this counter-torque is what dampens its precession. The top is more stable at higher angular speeds, and has a greater angular momentum at higher speeds. Torque is proportional to the change in angular momentum with respect to time, not the magnitude of angular momentum, so why is there a greater counter-torque at higher angular speeds?

    Also, I don't understand how the http://en.wikipedia.org/wiki/Gyroscope#Description_and_diagram" work to minimize external torques.

    Any help will be greatly appreciated.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 16, 2010 #2

    Cleonis

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    Gold Member

    Re: Gyroscope

    A brief version of the explanation is in the following physicsforums post (from me), about https://www.physicsforums.com/showpost.php?p=2697666&postcount=3".

    More extensive coverage is in the article about http://www.cleonis.nl/physics/phys256/gyroscope_physics.php" [Broken] on my website.

    It will make clear why higher angular velocity makes for a more stable gyroscope.

    The purpose of a gimbal mounting is to make the point of suspension coincide with the center of mass. The idea is to construct the gimbal mounting in such a way that the axes cross in a single point. Then that single point is the unique point of suspension.
     
    Last edited by a moderator: May 4, 2017
  4. Jun 19, 2010 #3
    Re: Gyroscope

    I'm confused on why the masses in the described quadrants will tend to move in the directions of the green arrows? Is the velocity of rotating around the swivel axis perpendicular to the angular momentum vector? What are inertial effects?


    http://plus.maths.org/issue7/features/gyroscopes/" [Broken]

    I don't understand how Newton's law of rotational motion implies that the angular momentum vector will move toward the torque vector. Where is the mounting in a spinning toy top/ what does the top precess around? Is the mounting the same as the point of suspension, and if the point of suspension coincides with the center of mass of the system, will the system not precess?

    "[URL [Broken]
    Gyroscope physics[/URL]

    gyroscope_physics_2.png

    I'm confused on why the particles in this example have acceleration in the given directions due to their angular momentum?
     
    Last edited by a moderator: May 4, 2017
  5. Jun 19, 2010 #4

    Cleonis

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    Re: Gyroscope

    attachment.php?attachmentid=24771&d=1270068885.png

    attachment.php?attachmentid=26541&d=1276934824.png

    Let me add another version of the picture.
    In the greyscale image two sections of the wheel are marked: 'dm1' and 'dm2'. They represent tiny sections. The behavior of the entire wheel arises from the behavior of all tiny sections combined.

    First concentrate on dm1.
    The wheel is spinning, at, say, hundreds of rotations per minute, and it is precessing slowly, say a couple of rotations per minute.

    Think of dm1 as participating in those two rotations, wheel spin and precession. In the images the precession is a swiveling motion around the vertical axis.

    The picture represents the moment that section dm1 is at its furthest from the vertical axis. As it continues to swivel the spinning will carry it closer to the vertical axis. Moving closer to the vertical axis there is a tendency to increase angular velocity around the vertical axis. (Just as in the case of a figure skater spinning up when she pulls her arms closer to her body.)

    Since dm1 is rigidly part of the entire wheel its angular velocity around the vertical axis cannot increase, but the tendency to move in that direction is there. Now consider the entire quadrant that includes section dm1. All parts in that quadrant are in the process of moving closer to the vertical axis of rotation

    Next dm2.
    The picture represents the moment that section dm2 is at its closest from the vertical axis. As the swivel continues the spinning will carry it away from the vertical axis. Hence there is a tendency to decrease angular velocity around the vertical axis. (Just as in the case of a figure skater slowing herself down by spreading her arms again.)

    In all of the quadrant that includes section dm2 there is a tendency to move in the direction of the arrow.

    Combining the tendencies of all four quadrants you get that the precessing wheel has a strong tendency to pitch.


    Note that this way of explaining gyroscope physics does not use the angular momentum vector of the spinning wheel. Attempts to use the angular momentum vector will make things more difficult. Don't burden yourself with unnecessary complexity.
     

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    Last edited: Jun 19, 2010
  6. Jun 20, 2010 #5
    Re: Gyroscope

    Thank you very much for your help. I have a few more questions.

     
  7. Jun 20, 2010 #6

    K^2

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    Re: Gyroscope

    Simplest demo. Imagine a rock on a string. You let it swing around the center in a circle. Now imagine that you give that rock a push perpendicular to its motion as it passes you. Where will the rock reach furthest deflection from the plane it was moving in? 90° ahead along the rotation. So pushing a gyro at one point, makes the end 90° ahead dip in exactly the same way.
     
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