It seems の doesn't always express possession as in 私の本.

What does it mean in such phrases as この役立たず and お兄ちゃんのばか?

And, what does の do in "埃だらけのテレビをちゃんと拭いてくれない？"?
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2015-03-20T03:41:19.800
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question
grammar
The meaning of の in この役立たず and お兄ちゃんのばか
の in 私の本 is different from one in この役立たず/お兄ちゃんのばか, but it is the same as one
in "埃だらけのテレビをちゃんと拭いてくれない？"

Most typical usage of の is like "(description) の (noun)", which the
description describe the noun, like "私の本" which means "a book(本) that belongs
to me(私)".

In case of の in この役立たず, "この" is one Japanese word and の is not an independent
word like "私の本". この means "this" or "such a". And 役立たず means a useless
thing/person, so it means "such a useless thing/person". You also can say just
役立たず, but put "この" together can emphasize on 役立たず. And it more sounds like the
speaker is frustrated of the thing/person because it is too useless.

お兄ちゃんのバカ is a Japanese slang usually used by young girls. To understand the
meaning, simply replace "の" with "は". The usage is like this: (a person) の
(negative word) A one of most famous example of this slang is from "My
Neighbor Totoro" by Studio Ghibli: メイのバカ。 (Mei, you are so stupid!)

Note that the usage of this slang is only to tell bad words in person, you
don't use this behind him/her.

の in "埃だらけのテレビをちゃんと拭いてくれない？" works the same as 私の本. Because 埃だらけ describes
テレビ. 埃だらけのテレビ: テレビ that is 埃だらけ = a TV that is covered with dust 私の本: 本 that
belongs to 私 = a book that belongs to me
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2015-03-20T05:22:18.877
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answer
Generally speaking you can think of の as a relation between sets, that can
translate to possession(of, 's), preposition(that, which) or more...

埃だらけのテレビ = the tv **which** is full of dust

お兄ちゃんのばか = the idiot **that** is my brother
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