A question about the trajectory of movement

[Ivan Nikiforov]

Good afternoon! I would like to ask for your help with the following question. Am I correct in understanding that the rotation of a circle regarding point A and the rotation of point A regarding the circle have different relative trajectories?

 

[DaveC426913]

I feel there is not enough information in your diagrams.

Which circle?
What motion?
How are the 3 diagrams related?
What do the arrows indicate?
What do the dotted lines indicate?

 

[Ivan Nikiforov]

Two points are conventionally highlighted on the blue circle. They are represented by small circles. The arrows indicate the direction from the center of the circle to the selected points. There is a point A next to the circle. Option #1: Point A is stationary. The circle is rotating. When it is rotated clockwise, the selected points rotate simultaneously. The upper point is to the right of point A, and the lower point is to the left of point A (Fig. 1). Option number 2. The circle is stationary. Point A rotates relative to the center of the circle. When it is rotated clockwise, the selected points of the circle appear to the left of the new position of point A (Figure 2). An observer at point A will see such a movement as the center of the circle moves along the trajectory of the orange line (Figure 3). Is this understanding of the process correct?

 

[DaveC426913]

This description is written with a chatbot. It describes one of the diagrams, but there are four diagrams.

Is there some reason why you can't label the diagrams themselves?

 

[berkeman]

This description is written with a chatbot.

That is not good. Thread is closed temporarily for Moderation.

 

[berkeman]

After a DM discussion with the OP, he assures me he did not use a chatbot for his posts in this thread. So the thread is reopened provisionally. Thanks for your patience.

 

[DaveC426913]

In have tried to re-diagram this for clarity.

Two points are conventionally highlighted on the blue circle. They are represented by small circles. The arrows indicate the direction from the center of the circle to the selected points. There is a point A next to the circle.

I have shrunk the circle-points to points.
I have added a label B to the second point and labeled the centre of the circle 'O'.
I have removed the arrows and antipodal points, as well as the orange circle until they are mentioned.
So far, what you have described is this:

Option #1: Point A is stationary. The circle is rotating. When it is rotated clockwise, the selected points rotate simultaneously. The upper point is to the right of point A, and the lower point is to the left of point A (Fig. 1).

OK, so B transforms from to the right of A to in front of A (from A's point of view, looking toward the bottom of the diagram).

Yes, all other points on the circle will likewise rotate clockwise about point A:

Option number 2. The circle is stationary. Point A rotates relative to the center of the circle. When it is rotated clockwise, the selected points of the circle appear to the left of the new position of point A (Figure

No, they will move clockwise. That is not always left in all cases.

2). An observer at point A will see such a movement as the center of the circle moves along the trajectory of the orange line (Figure 3).

The circle is stationary; you said so, above. It cannot move along any trajectory.

Is this understanding of the process correct?

I don't know. Do these modified diagrams help clear it up?

 

[Ivan Nikiforov]

Good afternoon! Thank you for your comment! I will try to explain the question in more detail. Points B and C are highlighted on the blue circle. Point A is located next to the circle (Fig. 1).

If the circle rotates clockwise, then points B and C rotate simultaneously relative to point O. As a result, point B is to the right of point A, and point C is to the left of point A (Figure 2).

If point A rotates counterclockwise, it moves to a new position where point B is to the right and point C is to the left (Figure 3).

Thus, from the perspective of the final positions of points A, B, and C, these two types of movement are the same. However, when point A rotates, points B and C do not rotate relative to point O. This is equivalent to moving the circle with points B, O, and C to a position to the right of the original position of point A. That is, we can say that for an observer at point A, the circle with points B, O, and C moves along an orange trajectory in a counterclockwise direction (Figure 4). Is this reasoning correct?

 

[DaveC426913]

Hello! Thank you for your comment! I will try to explain the question in more detail. On the blue circle, points B and C are highlighted. Next to the circle is point A (Fig. 1).

View attachment 362461
If the circle rotates clockwise, then points B and C rotate simultaneously relative to point O. As a result, point B ends up to the right of point A, and point C ends up to the left of point A (Fig. 2).
View attachment 362462

Point B ends up "to the right" of A from our overhead vantage point.

It is important we are clear whose "right" we are talking about, in any given scenario.

If point A rotates counterclockwise, it moves to a new position in which point B is on the right and point C is on the left (Fig. 3).

View attachment 362465

Hang on. "If A rotates counterclockwise" is ambiguous. An object rotating usually means "about its own centre point". What you mean is "If A is rotated about point O".

Thus, from the perspective of the final positions of points A, B, and C, these two types of movement are the same.

Great so far.

However, when point A rotates, points B and C do not rotate relative to point O. This is equivalent to moving the circle with points B, O, and C to a position to the right of the original position of point A.

"to the right of A" from whose perspective? Again, I think you mean "from our overhead vantage point".

And be careful with words such as "equivalent".

See below:

That is, we can say that for an observer at point A, the circle with points B, O, and C moves along an orange trajectory in a counterclockwise direction (Figure 4). Is this reasoning correct?
View attachment 362466

Well, an observer has an orientation. They are facing a certain way.


In the first scenario you start like this:

and end like this:

.

But in the second scenario, you start like this:

but end like this:

So, is it really "equivalent" for the observer at point A? That's up to you if you want to ignore their orientation - the induced rotation about their own center point.

I'd say you've got the geometry itself right, it's a question of being explicit in your descriptions of what's going on: do points have "orientation", or "directions of observation"? I would say a point does not, by default. But adding "observers" at the locations changes things.

It'll be fine as long as you are careful consistent in your descriptions. And - when you are breaking from an established consistency - explicitly state it.

 

[Ivan Nikiforov]

Thank you! Indeed, the points do not have an orientation or direction of observation. Only their final position and trajectory matter. In fact, this question is related to the observation of the electric and magnetic fields at points B and C, as well as at point A. The figure below shows the addition of magnetic induction vectors directed from point O to the circle. For convenience, only two opposite vectors are shown. As a result, when the circle rotates clockwise, points B and C move in opposite directions. As a result, the surface of the circle facing us becomes positively charged.

If point A rotates, the circle moves equivalently to the right and up without rotation. For point A, the upper half of the circle's surface is positively charged, while the lower half is negatively charged. As a result, the observer at point A sees a zero charge on the circle's surface. I believe this explains why my generator is not working. Thank you again!

 

[DaveC426913]

Cool. I think this has advanced from a generic geometry problem to a problem with a specific application.

I've reported the thread to see if the moderators agree that you might get better answer in a forum watched by those knowledgeable in electrical and magnetic induction principles.

 

[Ivan Nikiforov]

Thank you! I think that thanks to you, I found the answer to my question. The problem was in the field of geometry. When developing the design of the generator, I considered this process, but I made a wrong conclusion. I thought that if the final positions of the points were the same, then the trajectories and observed fields would also be the same. However, this turned out to be incorrect.