Connection between precession and resonance frequencies?

[Roo2]

I'm brushing up on my knowledge behind the physics of NMR. Turns out there was a lot I had misconceptions about; I thought it was very similar to absorbance/transmittance spectroscopy. I read some material about it which threw that idea out the window. I'm now looking at a video that shows a mechanical analogue of the phenomenon:



At about 5:20 in the video, the lector notes that in order to induce detectable precession in a "ground state" wheel, a torque must be applied that is perpendicular to the external torque (gravity) and of the same frequency as the precession frequency. He states that this is the resonance frequency and this confuses me greatly. Whenever I read about resonance, it was always in the context of a photon of a certain frequency which can induce a state transition. How then does this apply in the situation in the video?

I feel like I have all of the components of the explanation in my head but I just can't order them in such a way that they will make sense to me now, and again tomorrow when I wake up. I'm kind of grasping at the picture. I get that the perpendicular torque must change its direction at the same frequency (larmor frequency?) as the precession of the wheel. I get that this torque will then change the orientation of the wheel to a high energy state. However, there are many high energy states that can be achieved by the application of this torque. Can it still be the "resonance" frequency if it causes the wheel to go to between various states?

A-ha! The larmor frequency is the same no matter which orientation the wheel is brought to. Is this the trick I've been missing? The frequency of the torque that brings the wheel to any horizontal state is the same as that which will then bring it to the highest energy vertical state if it continues to be applied. Is that the key? Sorry, I'm sure this post is extremely rambly; I'm trying to fit all the pieces together in my head. If someone has the time, could you please lay it out for me simply?

P.S. Angular momentum is magic. You can come to me with all the formulae and cross products in the world that show L = I X w. You can tell me that momentum must be conserved. The fact that an L vector exists, and the "force" that drives its conservation is strong enough to keep the wheel vertical in face of gravity, is magic to me. It goes against all of my intuition.

 

[Cleonis]

P.S. Angular momentum is magic. You can come to me with all the formulae and cross products in the world that show L = I X w. You can tell me that momentum must be conserved. The fact that an L vector exists, and the "force" that drives its conservation is strong enough to keep the wheel vertical in face of gravity, is magic to me. It goes against all of my intuition.

Responding to the PS rather than to the actual question:

Since you use the word "wheel" I assume you are talking about macroscopic mechanics.
It is in fact possible to acquire an intuitive understanding of gyroscope motion. The key is to take advantage of the symmetries of the setup.


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]

At about 5:20 in the video, the lector notes that in order to induce detectable precession in a "ground state" wheel, a torque must be applied that is perpendicular to the external torque (gravity) and of the same frequency as the precession frequency. He states that this is the resonance frequency and this confuses me greatly. Whenever I read about resonance, it was always in the context of a photon of a certain frequency which can induce a state transition. How then does this apply in the situation in the video?

If memory serves me hydrogen nuclei have just two orientation states in the presence of a magnetic field: aligned and counter-aligned.

Of course that in itself cannot be understood/described classically. In terms of classical mechanics inbetween angles are possible too. Also, in terms of classical mechanics the counter-aligned state is inherently unstable.

Generally we don't know what the transition between quantum states is. For instance, when an electron shifts to another orbital level it's not a gradual process. If anything it's an instantaneous jump.

It seems to me that in that video the analogy is overstretched. I don't think it's helpful.