Conservation of momentum in gyroscopes

[gyroguy]

Not a scientist, please be nice :)

Let's assume I have a singe axis gyro (flywheel) spinning in space. I apply a force to a point which results in a change in pitch. I apply this force until the gyro is at 5* pitch and then stop.

Will the gyro continue to change pitch after the force stops?

If not, is the momentum from the pitch change conserved? How so? Or is there no momentum to conserve?

Thanks!

 

[jbriggs444]

If you apply a force (as opposed to a "couple") then the gyroscope will move linearly in the direction of the force in addition to changing pitch. It will continue to move linearly after the force is removed.

The changing pitch resulting from the applied force is a precession rather than a rotation. It has no associated angular momentum. So yes, there is no momentum to conserve.

 

[gyroguy]

If you apply a force (as opposed to a "couple") then the gyroscope will move linearly in the direction of the force in addition to changing pitch. It will continue to move linearly after the force is removed.

The changing pitch resulting from the applied force is a precession rather than a rotation. It has no associated angular momentum. So yes, there is no momentum to conserve.

So I am understanding that the pitch would remain the same 5* and the gyroscope would continue to move linearly?

 

[jbriggs444]

So I am understanding that the pitch would remain the same 5* and the gyroscope would continue to move linearly?

Yes.

 

[gyroguy]

Can you expand on this for something like a thrown football? When a football is thrown with the proper spiral the pitch of the nose will follow the arc. How does the pitch continue to change after the force of the throw has subsided?

 

[CWatters]

Humm. Good question. I suspect that they don't spin fast enough for the gyroscopic stabilising effect to dominate other forces such as aerodynamic forces.

 

[jbriggs444]

Humm. Good question. I suspect that they don't spin fast enough for the gyroscopic stabilising effect to dominate other forces such as aerodynamic forces.

That is my suspicion as well. However, I am unable to convince myself that there is no nutation going on. An object that is rotating and which is not spherically symmetric need not move in a pure rotation around its axes of symmetry (if any). It can spin and wobble. The angular momentum of such an object remains constant, but its orientation can have the visual appearance of undergoing a slow rotation.

[Mind you, this is outside the scope of a first year physics education which is the only formal training I've had]

 

[A.T.]

How does the pitch continue to change after the force of the throw has subsided?

There are still aerodynamic forces acting.