Can I use the relative pronoun "where" here?

Question

In articles I have see extensively that the pronoun where is used to relate something which does not have anything to do with places, locations, sites, etc.. Consider:

1. Newton's second law of motion is given by F=ma where m is the mass, and a stands for the acceleration. ( concocted by me )

2. Furthermore, the incompatibility of timber growing and cattle grazing seems obvious where either of these two industries is to be conducted under intensive management. ( google book )

3. He grew up in a family where what he was supposed to be when he grew up was clear: he was to be an electrician ( google book )

4. Furthermore, the linear quadratic problem has been studied for systems where the evolution of the state is described by partial differential equations ( google book )

It seems that we can use where to describe a sentence, a procedure, a supposition and many things. Am I right? Would you provide me with more insights about this pronoun. With this regard, can I always describe something done by others, especially by researchers, using where?

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Additional Information

What is "describing something done by others, especially by researchers"?

Consider you are asked to conclude your research on a topic in the shape of research papers. So, at the beginning of the paper you start with introducing why it is important to research about that topic and review the previous works having similar topic. In this context, you summarize their work and discuss about their results to demonstrate why further investigation or studies is important. Thus, you need to describe sentences, procedures, suppositions, models, figures, assumptions, criteria, and others of that ilk. So, I want to know can I always use the pronoun "where" to describe/justify/paraphrase (relative clause) the previous works?

For example:

They considered X where the authors neglect the Y.

X has been done where the marginal parameter Z was not taken into consideration.

Answer 1

• Where often refers to a physical place, but it can also refer to something like situation. Why is a situation considered a "place"? Logically because a situation usually consists of some type of "area", explicit or assumed - within that area things are part of the situation and outside of that area things are not.

• Arranging or defining things tends to be considered to happen logically in a "space", which is described using location words.

Newton's second law of motion is given by F=ma where m is the mass, and a stands for the acceleration.

The way I think about it, the word where here can be said to be "placing" or "arranging", in an abstract sense, definitions of m and a within or among the earlier phrase F=ma.

Furthermore, the incompatibility of timber growing and cattle grazing seems obvious where either of these two industries is to be conducted under intensive management. ( google book )

In situations where these two industries are to be conducted under intensive management (we are drawing a line between these two industries + being conducted under intensive management versus anything else not fitting this criteria), the incompatibility of timber growing and cattle grazing seems obvious.

He grew up in a family where what he was supposed to be when he grew up was clear: he was to be an electrician ( google book )

He is in a situation where he grew up in a family that made clear what he was supposed to be when he grew up (we are drawing a line between belonging to his family and being outside of the family), and therefore he is to be an electrician.

Etc.

Answer 2

The first example is in fact an innocent straightforward location-type where. The formula is somewhere in a book, on a blackboard, in your notes, on a screen, and it is there where you should think "energy" when you see the glyph E.

I have noticed the misunderstanding in various places. This probably arises because the formula is also (or even primarily) an abstract thing that expresses a fact or theory about our universe, an abstraction that is itself quite independent of the letters used. But an actual mathematician does not use letters at all when thinking of formulas: the abstraction is mentally represented directly, without the need for intervening glyphs. So the latter only make an appearance when the mathematician has to write the darn thing down - somewhere.