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Cassis
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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?
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 is the point at which the entire weight of an object can be considered to act. It is the point where all the forces of gravity on an object can be balanced.
The center of gravity for a circular wire can be determined by finding the point where the wire would balance if it were placed on a fulcrum. This can be done by hanging the wire from different points and marking where it balances, and then finding the midpoint between those marks.
The center of gravity is important because it affects the stability and balance of an object. If the center of gravity is too high or too low, an object may be more likely to tip over or become unstable.
The shape of a circular wire does not affect its center of gravity. The center of gravity is determined by the distribution of weight, not the shape of the object.
Yes, the center of gravity of a circular wire can change if the distribution of weight changes. For example, adding or removing weight from one side of the wire can shift the center of gravity to a different point.