Hej alla!
It took me a while but finally I will try to explain how to use small words with big meaning – nog, väl and ju. A reader brought up the subject with the following question:
” Hi,
Just had a lesson on how to use Nog, Väl and Ju, but my teacher was no very clear on what is the meaning of them. She said it was impossible to translate them directly to Swedish. Nevertheless, I believe there should be some kind of rule or at lest trend, rather than just doing it by “feeling” as my teacher said.”
First of all nog, väl, and ju are all so called satsadverb (sentence adverbials). Those of you who have read previous posts about word order and adverbials, know that a satsadverbial is a word that changes or specifies the meaning of the whole clause or sentence. Examples of satsadverb that might be more familiar to you are inte (not), kanske (maybe) and bara (only).
nog
“Nog” is a troublesome little word since it has several different meanings and can easily be misunderstood and misinterpreted, even by native speakers I dare to say. Myself I really had to think hard what nog really means in different examples. That might be an explanation to why teachers often say that it is a question of “feeling for it”.
I would say that a translation of “nog” goes from the weaker förmodligen – probably to the stronger visserligen – to be sure, it is true:
förmodligen – probably weak
säkerligen – no doubt, doubtless
helt säkert – certainly
visserligen – to be sure, it is true strong
Here are a few examples of how “nog” can be used:
Det blir nog sent i kväll.
(It will probably be late tonight. I will probably come home late tonight.)
In this case “nog” has the weaker meaning as in “I’m not sure, but probably”.
Det ska du nog inte räkna med.
(I wouldn’t count on it.)
Here the speaker is not 100% sure, but pretty close. I would say that the “nog” in this sentence means that the speaker has some doubts, but is more sure than if using “probably”.
Det ordnar sig nog.
(It will be alright, for sure.)
This should not be interpreted as “It will probably be alright”, which would be a strange thing to say I guess, not that encouraging 
In this case “nog” means “I’m sure of it”.
väl
Väl is a sentence adverbial that makes the sentence end up somewhat in between a statement and a question. I’ve had many students during the years being very frustrated over this. They ask me: ”Is it a question or not? I want to know!” And all I can answer is: “Well, it is sort of a question, but still not quite.” 
Stäng fönstret!
(Close the window!)
This is a command. You will go and close the window.
Du kan väl stänga fönstret.
(Why don’t you close the window.)
This is a little softer, rather an expectation or a wish than a command.
Kan du stänga fönstret?
(Can you close the window?)
This is, as you can see, a plain question.
Here are a few more examples with “väl”:
Det är väl inte hela världen.
(That’s not the end of the world, is it?)
“Väl” here corresponds with the “is its?”
Nu ska det väl snart sluta regna.
(It should stop raining soon, shouldn’t it?)
Det vore väl underbart om …
(Wouldn’t it be wonderful if…)
One thing that can be tricky with “väl” is that it is used when the speaker want to request something or give you an order so to speak, but still want to be polite. So the order can be mistaken for a question. This way of using “väl” is common in a work situation or in school. At work for example, your boss might say :
Du kan väl skriva klart den där rapporten till på måndag morgon.
This is a polite way to say “Finish this report, I want it in Monday morning.”
Your teacher might say:
Ni kan väl titta på den här artikeln till i morgon.
What the teacher really means is “Read this article for tomorrow.”
ju
The turn has come to “ju”. As I explained in a previous post, “ju” expresses something like “as you know” or “I know that you know”. Actually it is used a lot when the speaker thinks that the listener should know better. Some examples:
Va?! Köpte du en sprillans ny BMW? De kostar ju en hel förmögenhet.
(What?! Did you buy a brand new BMW? You know they cost a whole fortune.)
- Du tog väl med dig ett paraply?
(You brought an umbrella, didn’t you?)
- Nej.
(No)
- Men, jag sa ju att det skulle bli regn.
(But I told you it was going to rain.)
- Vill du ha en cigarrett?
(Do you want a cigarette?)
- Nej, jag har ju slutat röka.
(No, I told you I’ve quit smoking.)
Phew, this was a tough one! I hope a have clarified something for you. Please post questions if you have any!
