Question

An object of mass has three dimensions of size. Spin along any one of these dimensions is simple rotation. Can a single object have similtaneous spin along each of these three dimensions?

Answer 1

Maybe this will help. Suppose we are talking about a perfectly spherical object orbiting a larger perfectly spherical object, in a perfectly spherical orbit. (In this scenario, the center of mass is the same epicenter, for either object, regardless of angle relative to the other.

Now imagine a line drawn through the two centers of mass, and visualize how that straight line may be viewed as sweeping around the center of the larger mass in the way that a second hand sweeps around the center of a clock face. And picture the smaller object as spinning around that line as axis A of its rotation.

Next, imagine a line drawn perpendicular to that sweeping line. and passing through the center of the smaller sphere. Let us call that axis A. But wait, it is not just one line. It is, instead, an infinite number of interstitial lines swept over as the axis A line sweeps around the larger sphere as viewed from just one dimensional plane of the larger sphere. So let us see that the axis around which the smaller sphere is spinning is not one straight line, but as many as we wish to divide up the full circle of sweep into. We can readily see that the smaller sphere can be rotating around each of two axes axis A and B. but relative to the larger sphere, axis A is not part of just one line, but progressively passes through all the possible lines that can be drawn through center of the larger sphere and center of the smaller sphere.

Rotation CAN be going on in the single smaller sphere, along two axes simultaneously.

To imagine axis C of the smaller sphere as having a line drawn through its center, perpendicular to each of axis A and axis B. But the orbiting smaller sphere cannot be sweeping simultaneously both along the plane of axis B and along a plane of an axis C. It can only be sweeping in one plane or the other plane.

Let that sink in a bit and then imagine that the smaller sphere consists of many individual points which, for it to spin, must rotate, each in a circle around the smaller sphere's center. Thus, each corpuscule, or molecule, or point, or whatever we wish to think of as being any part of the smaller sphere other then its one center, cannot rravel along each of two tangential planes that are perpendicular to each other similtaneously.

Things get even more complicated when we take into account that axes can wobble, relative to a fixed line, even as they can sweep across fixed lines. When an axis wobbles, this we call precession. The earth precesses in its spin along its main axis, but that does not contradict that a single sphere (or any other object) cannot have parts that are traveling simultaneously along two perpendicular planes. If an axis is sweeping RELATIVE TO some other straight line, or if it is sweeping RELATIVE TO some other straight line of reference, this is a variance over time in the direction of an axis relative to some OTHER line of reference, whether real or imaginary.

If you have read an explanation of this answer anywhere else, ever, please let me know, because i have not found it explained anywhere. I had to think about it for many, many hours to think it through.

Have I made it clear to you?

If so, and if this is the first time you ever grasped it, let me know. ( : > )

Answer 2

Oh, by the way, if you think I deserve a point for giving what you think is the best answer to my own question, I need points to get out of the rank of a naive newbie.
( : > )

Answer 3

Not interesting? I was hoping someone would find at least one flaw in my explanation. Further thinking on it: The smaller object can be keeping one "face" to the larger one at all times. If it's doing that, then it'x making one revolution of spin for each orbit cycle. That's what Earth's moon is doing. It spins around a moving axis that is stable for itself, but constantly changing in relation to the location of the large object. In degrees, we would say the moon is spinning on an axis that is always perpendicular to the constantly sweeping line from Earth's center through moon's center. (Actually, such centers would only be constant if, as stated above, were perfect spheres and the orbit is perfectly spherical. None of these three conditions is met. But we can do this mind experiment on basis of "let's suppose." (Many problems and solutions assume something that is convenient for mathematical purposes, but not exactly what occurs.

Let me give just one example: Suppose we are asked on a test how long it will take an automobile, traveling 60 mph to go from one city to another city. For that to happen literally, that car would have to accelerate to 60mph before it left city A, and would have to continue without any slowing down, speeding up or stopping. Obviously, that would not happen. It would require running stop signs and traffic lights, speeding through slow speed zones, running into any vehicle that would get in the way, traveling in a straight line... So, when we are asked such a question on a test, we are expected to simplify to a point of absurdity in the real world.

So, too, must we simplify in speaking of the moon's shape, earth's shape and shape of the moon's orbit around the earth, or we would need a supercomputer to "tell it like it really is."

Allowing for simplification to the basic lines and axes, won't somebody critique my clutzy effort to describe the physics issues surrounding this question?