what does “rotate within the plane of the surface” mean?

A rotates within the plane of the surface of the support. what does it mean?

and one more question.

"A and B move with respect to each other"

in this sentence, A and B both move ? or when A moves B rests? Thanks in advance.

• The first section is more maths than english – WendyG May 20 '19 at 9:50
• I think you will get better answers at the StackExchange Mathematics forum [math.stackexchange.com/] – Peter Jennings May 20 '19 at 18:37
• I'm voting to close this question as off-topic because it's a math question. – Hot Licks May 20 '19 at 22:15

A rotates within the plane of the surface of the support.

As I read it, this sentence breaks down to the following:

There is a support structure of some kind.
This support structure has a (presumably flat) surface, which defines a plane (the geometrical kind).
A thing called A has this plane as plane of rotation, i.e. A rotates around an axis perpendicular to plane, on top of (or flush with) surface.

A and B move with respect to each other

There are two things, A and B, which (can) move relative to each other

• You said "...(possibly, but not necessarily) on top of surface." I would disagree with, that. To me "A rotates within the plane of the surface of the support" implies that A is recessed within the support. An example would be the famous rotating stage of the London Palladium which, unless the rotating part is actually moving, functions as a perfectly normal stage because the surface of the moving part is flush with the fixed part. – BoldBen May 20 '19 at 12:44
• @BoldBen agreed; given that no 3D object can really rotate within a plane, I guess, flush is the next best thing – glissi May 20 '19 at 13:00

It's heavy on mathematical jargon, and it is not exactly clear what mechanism is being described.

In plainer (!) words, we could say "A rotates on an axis perpendicular to the surface of the support" (or "on a plane parallel to the surface of the support"), and "A and B move relative to each other".

It is not clear whether A and B can both move at the same time relative to a third referent or not, or even whether they both can move at all relative to a third referent (since the free movement of only one is sufficient to satisfy the criteria of relative movement between the pair).

Suppose that A and B are hands on a watch, and that for the sake of argument, they lie in the same plane as the watch face.

We could abstract this further and define A and B using points. We introduce a point O to indicate the point around which the hands rotate. We define point A as being at the tip of hand A, and point B as being at the tip of hand B.

Hand A can then be represented as the vector from point O to point A, and hand B by the vector from point O to point B.

Surface of support is a technical term that occurs in more than one discipline, but that doesn’t matter here. So long as we are only talking about the three points A, B and O, we can define a plane from the triangle in space that they define.

Any movement of A relative to B can be described as a rotation in the ABO plane, and is measured by the angle between the two vectors.

Expressed in terms of a watch and its hands: you can move the watch as much as you like, but a change in position or orientation won’t change its telling of the time. The hands always rotate in the plane of the watch face.

My guess is that the OP’s question is drawn from a problem with more than two points and a hypothetical origin. Although one can talk about rotation when the plane of rotation is free to move, in many cases the plane will be more constrained. Instead of a watch on a wrist, the situation might be more like a clock on a wall, or the movement of two chairs on Ferris wheel. Without additional detail it’s hard to give a really good answer.