This isn't difficult to do. A key ring is a circle of wire - have you ever noticed anything like infinite forces trying to take your keys put of your pocket?Cassis said:The center of gravity of a circular wire should be in its center? What would happens if we put a marble and a wire into an empty space. Would the gravity force skyrocket as the marble approach the wire center of gravity?
The inverse square law applies to the exterior of spherically symmetrical sources.Cassis said:The center of gravity of a circular wire should be in its center? What would happens if we put a marble and a wire into an empty space. Would the gravity force skyrocket as the marble approach the wire center of gravity?
Depending on the relative size and the orientation of the ring, the system could oscillate about the barycenter of the pair, or they would collide, to finally settle, looking like a miniature Saturn with one wire ring.Cassis said:What would happens if we put a marble and a wire into an empty space.
Hm. Larry Niven thought so too. He wrote an essay on it, then followed up with a novel. That is, until his fans (many of whom of whom are mathematicians) disagreed. Niven had to write an entire sequel to Ringworld just to ret-con the engineering.Baluncore said:Depending on the relative size and the orientation of the ring, the system could oscillate about the barycenter of the pair, or they would collide, to finally settle, looking like a miniature Saturn with one wire ring.
OK, but the OP did not specify a relative diameter, nor any nudge away from perfect stability.DaveC426913 said:A mass at the centre of a ring of mass is not stable. Given any nudge it will drift away from the centre until the centre and the ring touch.
Yes this is what unstable usually means. If you place the mass at rest inside the ring, off-center, in the plane of the ring, there should be no oscillation, just a crash into the inside of the ring.DaveC426913 said:Yeah, that was kind of what i was trying to point out. Unless I'm wrong, a ringed sphere is not only unstable, it is a positive feedback loop. Like a ball balancing on another ball. Even a miniscule deviation from exact centre is magnified and accelerated.
The center of gravity of a circular wire is the point at which the entire weight of the wire can be considered to be concentrated. For a uniform circular wire, this point is at the geometric center of the circle formed by the wire.
To determine the center of gravity of a circular wire, you can use symmetry considerations. Since the wire is uniform and circular, the center of gravity is located at the center of the circle. This is the point equidistant from all points on the wire.
The center of gravity of a circular wire is at its geometric center because the wire is uniformly distributed along the circumference. This symmetry means that the weight is evenly distributed around the center, resulting in the center of gravity being at the center of the circle.
For a uniform circular wire, the center of gravity does not change and remains at the geometric center. However, if the wire is not uniform (e.g., if it has varying density or thickness), the center of gravity can shift from the geometric center to a point that balances the distribution of mass.
The shape of the wire significantly affects its center of gravity. For a circular wire, the center of gravity is at the geometric center. If the wire is bent into different shapes, the center of gravity will shift to a point that balances the mass distribution of the new shape. The specific location depends on the wire's configuration.