I know that If both elements are inanimated one can use the preposition of but not necessarily, example: "This is my car door" or "This is the door of my car" As far as I know, it would be wrong to say: "This is my car's door"-
Here is my doubt: "Today's work was hard!" or "Tomorrow's party is going to be brilliant" I believe these two sentences are correct.
If I can say "This is my car door" why sounds so weird to me to say: "Tomorrow party" or "The party of tomorrow"?
This stackexchange article is a good reference..
Michael Swan writes in Practical English Usage (2005.441-2) "With nouns which are not the names of people, animal, countries, etc, 's is less common, and a structure with a preposition (usually of) is more common." However, he adds "... both structures are possible in some expressions. [..] Unfortunately it is not possible to give useful general rules in this are: the choice of structure often depends on the particular expression. "
As he mentions, "it is not possible to give useful general rules", so what's applicable to the word "tomorrow" is not necessarily applicable to "car", and vice versa. The answer is: each case is different.
By the way, you can avoid the potential problem with "Today´s work was hard!" or "Tomorrow´s party is going to be brilliant" by using some other common expressions instead:
"The work today was hard!"
"Today the work was very difficult".
"The party tomorrow is going to be brilliant!"
"Tomorrow, the party is going to be awesome!"
The Guide to Grammar and Writing website, sponsored by the Capital Community College Foundation, says this:
Many writers consider it bad form to use apostrophe -s possessives with pieces of furniture and buildings or inanimate objects in general. Instead of "the desk's edge" (according to many authorities), we should write "the edge of the desk" and instead of "the hotel's windows" we should write "the windows of the hotel." In fact, we would probably avoid the possessive altogether and use the noun as an attributive: "the hotel windows."
However, it goes on to add that "this rule (if, in fact, it is one) is no longer universally endorsed".
So it isn't a rule as such, but the fact that you are asking this because it sounds odd is in line with the fact that many would avoid saying or writing "car's door", for example.
To my ears, as a native British English speaker, "car's door" sounds wrong because not only is the car an inanimate object but so is the door. The entire name of the door is "a car door". Likewise, a stereo in a car is "a car stereo". When you see such devices in a store, not yet installed in a car (so certainly not "belonging" to any car), they are still "car stereos". Once installed, you wouldn't say "my car's car stereo". In fact, I would argue that you wouldn't say "my car's stereo" either, because if it belongs to anybody, it belongs to you - along with the car. You'd say "my car stereo". You will probably find that this is the case with most examples of inanimate objects.
In contrast though, "tomorrow's party" is not the name of a party. It is just a party that is happening tomorrow. Also, "tomorrow" is not really an object. It is an abstract noun. It is quite common to use it with the possessive, for example:
"Worry does not take away tomorrow's troubles."
