Transition from inertial to circular motion

[Dale]

Yes, it would change its shape in any given inertial frame, but remain Born rigid.

 

[analyst5]

Yes, it would change its shape in any given inertial frame, but remain Born rigid.

Is there a threat of Ehrenfest paradox in this kind of motion? And could you perhaps compare what does happen in rest frames of the points undergoing circular motion, in the context of the distances between them staying constant. In one thread in the past I understood what happens in an accelerated frame in the context of staying or not staying rigid, but in this case I just don't understand the different perspectives and how does the body change its shape in different IRF-s, but has a constant shape in its own frame?

 

[Dale]

Is there a threat of Ehrenfest paradox in this kind of motion?

No, there is no rotation, so the effects of rotation, like the Sagnac effect, are not present.

And could you perhaps compare what does happen in rest frames of the points undergoing circular motion, in the context of the distances between them staying constant.

In the momentarily co-moving inertial frame the distances are constant.

In one thread in the past I understood what happens in an accelerated frame in the context of staying or not staying rigid, but in this case I just don't understand the different perspectives and how does the body change its shape in different IRF-s, but has a constant shape in its own frame?

Born rigidity is not defined in terms of the object's own frame since its own frame is non-inertial and there is no standard definition of a non-inertial object's frame. It is defined in terms of distances between points that are close together in the momentarily co-moving inertial frame. That frame changes at every instant.

 

[WannabeNewton]

Is there a threat of Ehrenfest paradox in this kind of motion?

Only if you take an extended body in uniform motion (e.g. at rest relative to a global inertial frame) and try to put it into uniform circular motion about some fixed axis. This is simply because the points of an extended body already in uniform circular motion can be equivalently represented by points on rigidly rotating disks.

 

[Dale]

Hi WBN, analyst5 is talking about acceleration without rotation. As the object accelerates it always faces the same direction in an inertial frame. Such an object would not be at rest in a rotating reference frame, even if it were accelerating in a uniform circular path, (i.e. it would rotate in the rotating frame).

 

[WannabeNewton]

Oops, sorry! I thought analyst was referring to the situation in the thread title.