Counter-torque in the gyroscope to oppose the torque

[GRB 080319B]

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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.

 

[Cleonis]

I'm confused with what is causing the counter-torque in the gyroscope to oppose the torque by gravity.

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" 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.

 

[GRB 080319B]

I agree that it should be possible to explain without invoking angular momentum. The explanation comes from the physics of gyroscopic precession.

The thing is, the case of a spinning gyroscope is simpler, because the gyroscope wheel is gimbal mounted. The suspension point coincides with the center of mass, and that symmetry is quite helpful. I will discuss only the case of a spinning gyroscope, followed by outline of how to translate to the case of the rolling hoop.

In the quadrants where the wheel's mass moves towards the swivel axis a force is required to reduce the velocity of rotating around the swivel axis. If that force isn't present the mass in that quadrant will tend to move in the direction of the green arrows in the image.
In the quadrants where the wheel's mass moves away from the swivel axis a force is required to increase the velocity of rotating around the swivel axis. If that force isn't present the mass in that quadrant will tend to move in the direction of the green arrows in the image.
The inertial effects in the four quadrants combined give rise to a tendency to pitch.
http://www.cleonis.nl

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/"

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
Gyroscope physics[/URL]

I'm confused on why the particles in this example have acceleration in the given directions due to their angular momentum?

 

[Cleonis]

I'm confused on why the masses in the described quadrants will tend to move in the directions of the green arrows?

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.

 

[GRB 080319B]

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

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

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 [i]angular momentum vector[/i] of the spinning wheel. Attempts to use the [i]angular momentum vector[/i] will make things more difficult. Don't burden yourself with unnecessary complexity.[/QUOTE]

I understand that the moment of inertia of the particles moving closer to the vertical axis is decreasing, which makes the particles rotate around the vertical axis faster. I understand that the moment of inertia of the particles moving farther from the vertical axis is increasing, which makes the particles rotate around the vertical axis slower. My confusion lies in how these tendencies are causing the particles to move in the directions of the arrows and cause the pitching. Are the particles following the orbit around the vertical axis for their given angular velocity, and if so, how can they if the wheel is rigid with a constant angular speed?

Also, I was unable to determine why higher angular velocity makes for a more stable gyroscope from your article.

 

[K^2]

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.