**EDIT:***As per Derek's comment, I have misunderstood the meaning of copula. My examples here were all ending particles (jp: 終助詞).*
The {Noun/なAdj}-なの or {いAdj/Verb}-の ending particle has various usage, and according to くろしお出版's 日本語文型辞典, the primary users are different according to usage.
Question
Used to indicate inquiry. Inclining intonation.
User: Children as general, or ordinary people towards their close ones (friends, family).
てつお:明日どこか行くの?
Tetsuo: Are you going somewhere tomorrow?
Explanation
To explain a circumstance. Declining intonation.
User: Children, female people. Light mooded.
かなこ:うん、町内会でちょっと用事なの。
Kanako: Yeah, I've got something up with the neighbourhood association.
Assent
Confirmation expression. Intonation can be either inclining or declining.
てつお:へえ、かなこちゃんってよく町内会に参加してたの。
Tetsuo: Wow, Kanako's quite active in the association, huh.
You can see that it implies a certain degree of surprise of unexpectedness.
Light volition
To express volition, either an order or a prohibition, in a light manner. Declining intonation.
User: female, towards someone of lower rank (e.g. younger people).
かなこ:そうよ。てっちゃんもいい加減町内会をサボらないの。そんなんだからいつまでたっても人見知りなのよ。ほら、明日一緒に行くの。いい?
Kanako: That's right. And Tec-chan, you ought to stop skipping association meetings. That's why you are always shy of other people. Come on, you should go together tomorrow. Oorah?
See how the の ending particle can be replaced with similar ones. I'll be using polite form for each:
- 明日どこか行きますか。 (の→ですか)
- (a) はい、町内会で少し用事があります。(の→です)
(b) はい、町内会で少し用事があるからです。(の→だからです)
- そうですか、かなこちゃんはよく町内会に参加していましたか。(の→ですか)
- てつおさんももう町内会をサボらないでください。({verb}ないの→{verb}ないでください
- さあ、明日は一緒に行きなさい。({verb}の→{verb}なさい)