Property of for same acceleration

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The discussion centers on the concept that two connected bodies accelerate together, such as a person in an accelerating elevator, which is referred to as "rigid motion" or "Born rigid motion" in relativity. This property implies that if one body accelerates, the other does as well, provided they maintain a fixed distance and orientation. The conversation questions whether this principle has a specific name or is simply an intuitive understanding of motion. It emphasizes that the connection, such as a rope or string, must not stretch for the same acceleration to apply. Overall, the concept highlights the logical relationship between connected objects during acceleration.
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Does the property that two bodies connected together and if one of them is accelerating with some acceleration the second also accelerates with the same acceleration, have a name? Like for example, if there is a person in an elevator and the elevator is accelerating with acceleration ##a##, then the person also accelerates with acceleration ##a##. Is there a name for this property? Or is not a property because it is so logical that it is said so because it makes sense?
 
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When to masses are connected with a rope or string, the condition is that the rope or string not stretch.

More generally, there needs to be a fixed distance and orientation between the two objects the for their acceleration to be the same.
 
Dr. Courtney said:
When to masses are connected with a rope or string, the condition is that the rope or string not stretch.

More generally, there needs to be a fixed distance and orientation between the two objects the for their acceleration to be the same.
What about the case for a person inside an accelerating elevator?
 
It is called rigid motion or, in relativity, Born rigid motion.
 

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