Transition from inertial to circular motion

[analyst5]

So what about the scenario I mentioned in my previous post?

 

[Dale]

Since it is not rotating it can be accelerated arbitrarily and remain Born rigid.

 

[analyst5]

Since it is not rotating it can be accelerated arbitrarily and remain Born rigid.

And how will some IRF perceive the process of undergoing circular motion? Let's call that frame the initial frame and let's suppose that the object is first traveling with 200 km/s linearly and then with the same speed while circulating. The clocks would still dilate because of velocity, but what would happen with length contraction, would the coordinate length be different at each instant because at each instant the object is changing direction while traveling around the circle?

 

[Dale]

what would happen with length contraction, would the coordinate length be different at each instant because at each instant the object is changing direction while traveling around the circle?

Yes. (if I understood the question correctly)

 

[analyst5]

Yes. (if I understood the question correctly)

So the circulating body would remain rigid from the perspective of each point on the body (distances between the points would remain constant), but from the perspective of an IRF the body would be changing its shape during the turnaround because of length contraction that depends on the direction of the motion, which is changing in this case?

 

[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.