Feynman's wobbling plate: how to recover from burnout

"So I got this new attitude. Now that I am burned out and I'll never accomplish anything, I've got this nice position at the university teaching classes which I rather enjoy, and just like I read the Arabian Nights for pleasure, I'm going to play with physics, whenever I want to, without worrying about any importance whatsoever."

The full acceptance of burnout seems important. ie, rather than cling to old ideas about who you are and what you want, at a certain point it's best to let go of your ambitions and simply embrace life in whatever way you can. I remember one conversation I had on a bus in Thailand some years back:

"What do you do?" "Oh, I'm a burnout from China. I mean, I was starting a company there, and I sort of imploded. Oh, the business didn't fail, it's still running... I just failed. At being me."

It was the first time in my adult life that I didn't have an impressive story to tell about what I was achieving.

Failure, instead of driving people away (as I'd feared), led to more empathy and deeper relationships. And instead of harming my career, it gave me the freedom to explore my interests without the pressure to achieve, which helped me figure out what I really enjoy. I'm now working crazy hours again, but it's so well aligned with my values and interests that I rarely feel stressed. (And I take better care of myself, because I know what can happen if I don't.)

That was very insightful. Thank you.

I know this is kinda off-topic but could someone explain why the wobble rate and the spin rate of the plate would have a 2 to 1 ratio? Is this somehow related to the spin numbers of elementary particles?

This is completely off-topic, but I've been seeing this weird style of quotation marks occasionally for a while now. It uses two backticks at the beginning, and two apostrophes at the end: ``quoted''. If you're not using TeX, doing that will generally look pretty weird. So why do we still see it?

It's a little complicated, although not so complicated that it has anything to do with the spin of elementary particles.

The basic reason is due to perpendicular axis theorem. If you have a plate, there is some moment of inertia about the axis perpendicular to the plate, and a different moment of inertia about any axis in the plane of the plate. The perpendicular axis theorem says that the moment of inertia about the axis perpendicular to the plate is twice that about the axis in the plane of the plate.

Now, suppose you attach a rod through the plate, but at a bit of an angle, and then you spin the plate around this rod. As you can imagine, it'll take some effort to keep the plate spinning about the rod; it'll be rattling around trying to spin in a different way. Because you're not spinning it about any axis of symmetry, the angular velocity vector is not lined up with the angular momentum vector and so it requires some torque to keep the plate spinning around the axis you want. But if you're just throwing a plate up in the air, you can't exert any torque on it---it's just going on its own. So if the plate is spinning about some funny axis, it has to do so in a special way in order that the angular momentum vector lines up with the angular velocity vector.

So, draw a diagram of this lopsided plate turning around a rod. The angular velocity will have some component perpendicular to the plate and some component parallel to the plate so that the overall angular velocity is parallel to the rod. Let's suppose that the angular momentum vector's component perpendicular to the plate is exactly as long as the component of the angular velocity perpendicular to the plate. Because the moment of inertia in the plane of the plate is half that perpendicular to the plate, the length of the component of angular momentum in the plane of the plate is half the length of the component of angular velocity in the plane of the plate. As you can see, the angular velocity vector is not lined up with the angular momentum vector.

Now we decouple the plate from the rod so that it can also spin about an axis perpendicular to the plate. If we spin the plate about this axis backwards at half the speed it was originally spinning about this axis, the length of the component of angular momentum perpendicular to the plate is now half the length of the same component of the angular velocity. And so the angular momentum vector is now lined up with the rod that we're spinning the overall system around. But because the angular momentum vector and the angular velocity vector are parallel, there's no need to exert any torque on the system to keep it going. So we can remove the rod entirely and the plate will wobble in the air in a ratio of 2:1.