When center of rotation is atop center of gravity?

I'm still with SD's kid, saying that the prop doesn't stay at an angle purely because of balance, but because the balance is good enough that the small amount of friction provided by the pivot point is enough to keep it where it is. If there was no friction there whatsoever, the prop would level out, either by going horizontal to the surface, or by going vertical. Both outcomes would rely on gravitational pull on the tip of each blade, depending on the angle at which they're placed.

I may be wrong and I'm ready to face that if there's proof, but right now that's the only outcome that makes sense to my brain.

I get that, but on the ISS, the effects of gravity on the object are next to non-existant. That's why I've been staying away from "putting our object into space", so to speak. Yes, space is a friction free environment and as such would work perfectly to demonstrate that part of the physics, but it's also a gravity free (almost) environment, so it would put that part completely out of play and skew the results.

I have read, I am thinking hard, but that does explain it better than my Kid could, thanks.
So CG and CR..... ok... I get that.

Please, understand that the following is directed solely at the question stated originally in this thread, and is NOT directed to anyone who has another point of view on the matter:

Anyway, I am going to attempt to argue something along the lines of a "Squeeze Theorem", seen in Calculus. It's a kind of proof that is made using a limit-process to show that a particular value is found between two other ranging values.

In short, if we have a twisting force one direction (let's call it oriented in a negative "left" direction) that ultimately, smoothly, and continuously diminishes, and then becomes a twisting force oriented in the opposite, positive direction to the right. In doing that, the twisting force had to pass through something that was essentially neither force (a place of zero twisting force).

Now, what we have causing the twisting (torque) is an "apparent" weight. It's not a true weight, but the net weight as a result of all various forces involved (the junk that is oriented around the axis of rotation, wherein more of it is on one side than the other). This apparent weight is located in the center of gravity, or center of mass. Now, the Center of Gravity doesn't have to be in the center of length, as you may well know. If an item is heavy to one side, it has more mass on one side than another, even if both sides are of equal length. If the item on a swivel has more apparent weight on one side than the other, we pick up that twisting torque I just mentioned (let's say oriented favoring the left, at first).

If we start peeling away some of the layers of material, slipping the center of gravity slowly toward the other side (while not taking away from the item's overall length), then the twisting force becomes less and less, trending toward zero. If we take too much material off the left side, then the twisting could roll over the other way, and we get a right-oriented torque. So, as you can see, we decrease and decrease the left-sided twisting force to such an extent, wherein it could, ultimately, turn into a right-sided force if we don't watch it. In this case, it had to have passed through zero twisting force, in order to switch from Left-sided to a Right-sided force. (notice I am not saying right or left motion, but force. This force is the apparent weight held at the center of gravity, and the apparent weight becomes less and less on one side as we strip away stuff, until we've stripped away too much, turning the force through zero and on to the other side). This moment of force can actually be thought of as a horizontal length made between the center of rotation and the center of gravity. As we reduce the apparent weight on one side, the length of that moment “arm” of force becomes shorter and shorter on the left, passes through zero-length and then becomes a moment force, with some sort of length on the right side, if we take it all too far. When you have zero-length moment force, you have zero apparent weight. Things with zero weight (weightless) do not have torques turning them this way or that. Either side has a zero-apparent weight, or zero-net weight and, thus, the torque is a net of zero too (meaning a balance of torques).

And that's basically it. The decreasing force is called the decreasing moment of force, caused by a removal of the apparent weight of having too much stuff on one side. As this moment of force diminishes, it can pass through zero moment at some point, possibly moving over to the other side, turning the item the other direction with an opposite-oriented torque, if the removal of material on one side goes too far.

EDIT:

To take this to the extreme, I'll include a case where the object providing the predominant gravitational acceleration is, say, a black hole. Now, this situation HAS a place where the gravitational acceleration is greater, obviously greater, for a so called lower blade than it is for the upper blade. The reason I take it to this extreme is because I opted to discuss a frictionless pivot, or frictionless bearing. So, to make clear the probable outcome of a frictionless pivot, let's include a strong and obvious gravitational source.

Now, in this case, we can easily see that if we start with one blade at 45 degrees and the other down at 225 degrees, the blade at 225 degrees IS going to receive more acceleration than the other blade, and the result will be that this lower blade will swing side to side until it is perpendicular NOT horizontal. (Think of a propeller made of iron being lowered toward a magnet. Whichever blade is closer to the magnet will be pulled until pointing directly at it. This is NOT a horizontal orientation.)

The importance of this is that the two videos discussed as potential outcomes here predict either horizontal: like a balancing scale or sea saw. Or, stationary; the propeller staying wherever we left it. This extreme frictionless case I've just outlined provides for a totally different result than either of these two video choices.

Making the case for a horizontal outcome is only possible if the propeller is somehow carefully leveled, exactly at level with the surface of Earth and not bumped in anyway. Any other orientation results in nothing like horizontal. Especially not wiggling until horizontal, as the first video suggests. Instead, the propeller ends up vertical. So, the horizontal predictioon is significantly the wrong prediction.

And, lastly, the far less intense situation involving Earth and the propeller, (instead of a black hole and the propeller), results in arguably insignificant tidal forces; lending itself, instead, to an arguably significant "resistance to acceleration and motion" called inertia. In other words, the inertia present in the propeller's mass is likely going to prevent the insignificant tidal forces to do the job of starting the propeller moving, if we've stopped it at some orientation. So, the stationary prediction is arguably better between the two choices, but not perfect.

EDIT II

I'm thinking of a large-scale Cavendish Experiment to demonstrate much of this, instead of relying on magnets, as I was first thinking. However, the Cavendish Experiment employs lengths and radii large enough, with the right proportions within the torsion balance that they induce Tidal Force when nearer the larger mass. This is nessesary, otherwise the torsion bar doesn't move, (for the same reasons we're talking about in the "stationary" result). Would need one massive, massive ball and an extra, extra small pivoting torsion balance to get something on the order of proportion seen within an Earth-like object next to a propeller. A small enough torsion bar should deny anything like tidal forces and we get the stationary effect I'm describing. Problem is, then you have no proof there is any gravitational attraction going on, because your tiny torsion bar doesn't move or rotate. Might need two rigs: one to demonstrate Cavendish's attraction and the tidal forces working, the other to show a point where tidal force-like forces are no longer prevelant, using the much smaller torsion bar.

wouldn't lead be a better gravitational mass than iron as it is more dense and less magnetic?

and I think that's the key to the debate - are - I don't know if tidal forces can be used as a catchall, but for our purposes I'm going to use it that way - are tidal forces going to cause a long object to be biased towards horizontal or to vertical?

I think we have enough now to restate this better, starting it over in one of the show idea forums. It has a kernel question, based on commonly-held thoughts, beliefs and ideas. It poses new solutions and even a means for testing these conclusions by way of a uniquely-modified, somewhat updated 1798 experiment in physics. Such a test that the show could easily do. Heck, I may even try it, if I can get the funds together!

I've posted a query about moving this one, though I do wonder if the topic in general is interesting enough for the show.

If that's the way a majority feel here, I'll not spend the time reworking it into a cleaner thread in show ideas.

I'd hoped that taking a closer look at Cavendish, using levitation with magnets, vacuum and so forth would have put it into the Science portion the show is interested in.

So, if no one else objects, I'm thinking of calling the new thread "The Balanced Propeller Conundrum". Question remains, where exactly would it go? Random Ideas?

Thanks, TLW! Put it in Random Idea then?

I can't seem to pick a category for balancing something on a bearing. While balancing a tire might go into Transportation Myths, balancing a propeller might be a Transportation Myths too, but I doubt it??

I'll do a rewrite once I see how my College Chemistry class is going to go. First class today.