Let’s say you have two identical boxes. You pick up the first box and see nothing unusual about it. You then pick up the second box and notice some strange behavior. Whenever you tilt the box it seems to resist being tilted, and “squirms” in a strange way. Looking inside the boxes, you see a still gyroscope in the first one, and a spinning gyroscope in the second. Does this mean that the spinning gyroscope somehow has fundamentally different properties from the non-rotating one?
Before Galileo and Newton, it was believed that objects in motion were fundamentally different from non-moving objects. It was thought that moving objects possessed a property, called “impetus”, which kept them in motion and which slowly leaked away, causing the object to come to a halt. This has long since been disproved; yet substitute “angular momentum” for impetus and it seems to still be true for spinning objects. Or is there some broader principle in which all values of angular momentum, including zero, behave according to the same rules?
Right. And now it’s believed (established, really) that moving objects possess a property, called ‘inertia’, which keeps moving objects in motion and stationary objects stationary. (This is also known as ‘Newton’s First Law of Motion’) Inertia does not ‘slowly leak away’, but the motion it maintains can be taken away by application of force, in accordance with Newton’s second and third laws of motion. The principle of inertia and Newton’s other laws (applied to each particle of the rotating object) fully explain the behavior of the gyroscope, whether in or out of the box, rotating or stationary.
I don’t think so. The “different properties” are in the different motions of the gyroscopes, not inate in the objects themselves. The spinning object has angular momentum and the stationary object doesn’t. If the motion of the spinning object is stopped, the angular momentum disappears.
If I understand your question correctly, yes. All rotating objects are accelerating, i.e., they are changing the direction of their velocity vectors. Unlike objects moving in a straight line at a constant speed, rotating objects have no inertial frame of reference in which they are motionless. Their acceleration must be the result of a force, and when the force is no longer applied, they stop accelerating – that is, they stop rotating.
Suppose you open the weirdly-acting box and, instead of a gyroscope, you find a large oscillating mass riding back and forth on linear bearings.
I think that it’s not ANGULAR momentum which is weird. It’s just ANY acceleration that’s weird (linear momentum OR angular momentum.)
Or in other words, linear motion is fundamentally different than acceleration. Objects don’t have a single velocity. An object can have many velocities, since velocity is always measured between the object and an observer (so if the many observers are moving differently, the object will “have” many different velocities at the same time.) But an object has just one acceleration, and acceleration is intimately tied to gravitational fields. Velocity is not.
Or another way to say it: there is no “absolute” reference frame for velocity, but there DOES seem to be one for acceleration.
Are you familiar with Mach’s principle? It explains inertia as being caused by all the objects in the universe; the so-called “fixed stars.”
These various kinds of weirdness are included in the chapters on General Relativity. (I never got that far in physics myself, and only know a tiny bit.)
It is true that there is a force on the rotating gyro. It is the centripetal force that ultimately derives from the electric forces holding the molecules that make up the gyro together. An accelerated body will appear accelerated from the point of view of an unaccelerated coordinate system (inertial frame).
Maybe the OP is really asking why an inertial frame is different than an accelerated frame. After all, if I go out in the back yard and spin myself around, according to Mach all of the distant galaxies pull my arms outwards because I’m causing the entire universe to rotate around me. (I have little idea of how Einstein uses GR to explain the same thing. I only had undergrad courses, and they stop at SR.)