How exactly does a gyroscope relate to angular momentum?

[omgwtfitsp]

Wikipedia says that a gyroscope is based on the conservation of angular momentum. This whole day I'v been doing my report on gyroscopes and explaining their precession. But how do I connect the conservation of angular momentum to this? I don't know where to start.

I have seen videos demonstrating the conservation of angular momentum as people stand on turn tables with a spinning wheel, and as they turn the wheel, the wheel is resisting its change in orientation of its axle and will cause you to turn in the opposite direction to conserve angular momentum.

But how do I put this in terms of the gyroscope? Like, when the gyroscope is precessing, is it experiencing angular momentum?

 

[Curl]

How were you "explaining" precession without referring to angular momentum?

The precession happens because there is a torque on the body (from gravity, draw it). And a torque produces a change in angular momentum (similar to F=dp/dt but for rotation). It works using the right hand rule if you use classical coordinates.

 

[Cleonis]

Wikipedia says that a gyroscope is based on the conservation of angular momentum. This whole day I'v been doing my report on gyroscopes and explaining their precession. But how do I connect the conservation of angular momentum to this?

You are asking specifically about gyroscopic precession. As all sources mention, to have a state of gyroscopic precession the gyroscope wheel must be subject to a torque.

There is only one case where the angular momentum of the gyroscope wheel is conserved: when there is no torque. To avoid a torque on the gyroscope wheel you set up a gimbal mounting. The gimbal mounted gyroscope maintains the same orientation in space.

The angular momentum of a gyroscope in gyroscopic precession is not conserved. The angular momentum is changing all the time, due to the torque that is exerted.



To understand the mechanics of gyroscopic precession you need to be aware of how spinning objects respond to a torque that is applied on them.
That is, gyroscopic precession is all about change of angular momentum of the gyroscope wheel, rather than about conservation of angular momentum.

Let me refer you to an earlier discussion (by me) on physicsforums:
A post from november 2010 about https://www.physicsforums.com/showpost.php?p=2992527&postcount=3". Illustrated with images. Just a qualitative discussion.

More detailed discussion (including math) is in the http://www.cleonis.nl/physics/phys256/gyroscope_physics.php" article on my website.

 

[Cleonis]

I have seen videos demonstrating the conservation of angular momentum as people stand on turn tables with a spinning wheel, and as they turn the wheel, the wheel is resisting its change in orientation of its axle and will cause you to turn in the opposite direction to conserve angular momentum.

In the demonstration you refer to there is conservation of angular momentum of the setup as a whole: the turntable, the person on that turntable, the spinning wheel in the demonstrator's hands.

A turntable setup like that is not the same case as gyroscopic precession. The turntable demonstrations do not offer clues to help understanding what is going on in the case of gyroscopic precession.

 

[PJC01]

I can help clarify the connection between a gyroscope and angular momentum.

First, it's important to understand what angular momentum is. Angular momentum is a physical quantity that describes the rotational motion of an object. It is defined as the product of an object's moment of inertia (a measure of its resistance to rotation) and its angular velocity (how fast it is rotating).

Now, let's look at a gyroscope. A gyroscope consists of a spinning wheel or disk mounted on an axle. When the gyroscope is spinning, it has angular momentum. This is because the spinning wheel has both a moment of inertia and an angular velocity.

So, how does this relate to the conservation of angular momentum? The conservation of angular momentum states that in a closed system, the total angular momentum remains constant. This means that if there are no external torques acting on the system, the total angular momentum will not change.

In the case of a gyroscope, when it is precessing (changing its orientation), the conservation of angular momentum is at play. As the gyroscope precesses, the direction of its angular momentum changes, but its magnitude remains constant. This is because the precession is caused by an external torque, such as gravity or a person's hand, which is acting on the system. The gyroscope resists this change in orientation by conserving its angular momentum.

To summarize, a gyroscope relates to angular momentum because it has angular momentum while spinning and its precession is a demonstration of the conservation of angular momentum. I hope this helps clarify the connection between the two concepts for your report.