Gyroscopeic Precession: How Does Angular Momentum Arise?

[galbatorix]

Once the gyroscope starts to spin about the pivot it acquires an upward angular momentum. But since it did not have any angular momentum in this direction before, and the only torque is due to the gravitational force, how does this new angular momentum suddenly arise. Isn't this a violation of the conservation principle?

 

[Dale]

Rotational motion gets pretty complicated quickly. I believe that is not a new angular momentum, it is just the visible manifestation that the angular momentum does not lie exactly along the axis of the gyroscope, but is in fact pointing at a slightly steeper vertical angle.

 

[galbatorix]

@DaleSpam I found that a little vague can you please elaborate.

 

[Dale]

There is the axis of the gyroscope, meaning the material axis of the gyroscope about which it is symmetric. And there is also the angular momentum, which is a separate thing and is not necessarily aligned with the axis of symmetry.

 

[galbatorix]

But even if it were not vertical , it has a vertical component and this component again has no reason to be there.

 

[Dale]

Why not? You are assuming that the angular momentum initially lies along the symmetry axis. If you don't assume that then everything works out. So question that assumption.

 

[Physicist97]

Well remember, all conservation laws are under the assumption that it is a closed system and there are no outside forces acting on it. If I were to place a ball at the top of an incline and let it roll down, the system will suddenly have angular momentum when it did not before. This is due to the fact that it is in contact with the incline, producing a static frictional force and is thus not a closed system.

If that ball were to slam into another ball, neglecting loss of energy to heat and drag, and both balls were to start spinning, you could apply conservation of angular momentum to deduce their individual angular momentums given the initial angular momentum and the radius of the spheres, etc. Of course the spheres, over time would stop spinning due to air resistance, thus it is not a perfectly closed system.

You can apply this to the gyroscope. In order for it to gain angular momentum when it has none, it needs an outside force. Your hand giving it a spin or something like that. Over time the gyroscope will lose this angular momentum to air resistance, but if you were to account for the gain in angular momentum of every particle of air, you would find that it is conserved.

 

[A.T.]

Once the gyroscope starts to spin about the pivot it acquires an upward angular momentum.

Does it? If you stop applying a torque, the precession immediately stops, so where does the supposed upward angular momentum go?

 

[galbatorix]

@A.T. are you trying to say that there is no angular momentum in the upward direction?
the spinning wheel has mass and it is rotating about the pivot with some angular velocity in that direction due to precission doesn't that mean it has an angular momentum.

 

[A.T.]

are you trying to say that there is no angular momentum in the upward direction?

See the vector diagrams here:
http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html