Areyu:
Yes, Steve. I was precisely suggesting a "law or principle that crosses scales". And your response seems to be a proper way of trying to find a solution. You are suggesting a very general principle or "law", and any solution which applies on all scales, i.e. a universal principle, would have to be very broad and encompassing.
Yes, I think it's probably right to call it a "general principle" rather than a "law", because the idea of isotropy - of things that are the same in all directions - underlies many laws without being specific to any one of them. It has more to do with geometry than physics.
I think geometrical shapes like spheres and circles naturally arise from isotropy as a basic principle of geometry, before we even consider any actual physics, because the definition of a circle (2D) or sphere (3D) is that it is a shape which looks the same in all directions, from the point of view of its centre. It is the
definition of spherical symmetry on which the definition of isotropy rests.
And the definition of circular motion at constant speed is that it means constant acceleration towards the centre of the circle. So any force which causes the same amount of acceleration towards a central point will result in circular motion.
However, I have a question about your general principle of a force radiating from a point equally in all directions. I can see how it would apply when taken on a large scale, such as planets orbiting stars, and I can see how it would apply on the atomic scale, at least as far as electrons spinning around an atomic nucleus is concerned. But would it apply to just the general spinning that all subatomic particles do in relation to themselves, such as an electron just spinning round and round either as it orbits an atom or if it's standing alone in empty space? I am imagining subatomic particles in empty space spinning, but without orbiting anything else....
Well, you're talking here about "intrinsic angular momentum/spin" as opposed to "orbital angular momentum".
The intrinsic spin of something like an electron does not appear to share all the properties of intrinsic spin as we understand it to apply to objects like planets, but it is still first understood by (imperfect) analogy with these large scale objects.
I would say that the underlying principles which most help to describe the ubiquity of intrinsic spin are the extension of Newton's laws of motion from linear to rotational motion.
As I said, all objects are observed to keep moving at constant velocity unless acted on by a force (Newton's 1st law). This also applies to the
angular velocity of spinning objects because the centripetal force acting on every point in a spinning object is always exactly perpendicular to the direction of its velocity. As I said above, it is a fact of geometry that an object moving in a circle (such as a small part of a spinning object) is accelerating towards the centre of the circle. And the mathematics of vectors shows that if the acceleration is perpendicular to the velocity, it doesn't change the
speed. It only changes the direction. (Remember, velocity is both speed and direction. A vector.)
So it naturally follows that once an object is spinning, its rate of spin will remain constant until another force acts to speed it up or slow it down.
This might explain why objects that start spinning keep spinning, but it doesn't explain why all the stars and planets in the universe seem to be spinning in the first place. For that, you have the conservation of angular momentum.
This means that if a spinning object, or collection of things that will one day coalesce into an object, shrinks in size its rate of spin increases (as you can demonstrate by spinning round on an office chair with your arms and legs sticking out and then pulling them in). Since large collections of gas and dust floating through space are very unlikely to be entirely motionless, there will always be at least some small amount of net rotational movement. This gets hugely magnified when the gas and dust contracts due to mutual gravitation.
That, it seems to me, explains the ubiquity of spin in the large scale universe. But it doesn't explain the intrinsic spin of elementary particles, does it? The explanation of that, I think, goes into more sophisticated levels of physics than I'm qualified to confidently explain. I know my limits!