In section 12.3 on page 287 in connection with the Procedure: Extended free-body diagrams as exemplified by figure 12.11:
I would warn students that this is in some ways an abuse of the symbols. It is a trap for the unwary. Note the contrast:
In all diagrams in the book up to this point, an arrow has represented a vector. A vector, by definition, has a direction and a magnitude ... but not a location.
In figure 12.11, each arrow represents something more than a vector: has a direction and a magnitude ... and a partially-significant location!
This is a tremendous inconsistency. It can easily lead to profound misconceptions about the definition of "vector" and the definition of "force".
AFAICT, every textbook in the last 400 years has mishandled this issue. The best solution I've been able to come up with, after much struggle, is to carefully distinguish between a dynamic _interaction_ and a _force_.
-- In simple cases, we have: interaction = (force, line of action)
-- If we pick a datum, we can write: interaction = (force, torque)
The arrows in figure 12.11 are not vectors. We know that because a vector has direction and magnitude but not location, whereas each of these arrows has a partially-significant location.
In particular, the arrows in figure 12.11 are not really forces and should not be labeled "F", since force is a vector. Instead they should be identified as _interaction_ arrows and labeled with some appropriate symbol such as χ.
In any case, the distinction between (direction, magnitude) and (direction, magnitude, location) needs to be carefully explained. Just calling it an "extended" diagram does not suffice to explain in what ways the concepts are being extended.
In section 12.3 on page 287 in connection with the
Procedure: Extended free-body diagramsas exemplified by figure 12.11:I would warn students that this is in some ways an abuse of the symbols. It is a trap for the unwary. Note the contrast:
This is a tremendous inconsistency. It can easily lead to profound misconceptions about the definition of "vector" and the definition of "force".
AFAICT, every textbook in the last 400 years has mishandled this issue. The best solution I've been able to come up with, after much struggle, is to carefully distinguish between a dynamic _interaction_ and a _force_. -- In simple cases, we have: interaction = (force, line of action) -- If we pick a datum, we can write: interaction = (force, torque)
The arrows in figure 12.11 are not vectors. We know that because a vector has direction and magnitude but not location, whereas each of these arrows has a partially-significant location.
In particular, the arrows in figure 12.11 are not really forces and should not be labeled "F", since force is a vector. Instead they should be identified as _interaction_ arrows and labeled with some appropriate symbol such as χ.
In any case, the distinction between (direction, magnitude) and (direction, magnitude, location) needs to be carefully explained. Just calling it an "extended" diagram does not suffice to explain in what ways the concepts are being extended.
Possibly-constructive contribution: A discussion of this point, with diagrams, can be found at https://www.av8n.com/physics/force-intro.htm#sec-interactions and https://www.av8n.com/physics/force-intro.htm#sec-more-interactions