If 's shows possession then wouldn't it be used in the following sentences?
I want to buy a car's door.
You have broken my computer's screen.
If 's shows possession then wouldn't it be used in the following sentences?
I want to buy a car's door.
You have broken my computer's screen.
Although there is a degree of idiomatic preference with regards to these phrases and the (lack of) apostrophe-s, there is a more subtle bit of schema that helps to inform this choice.
The comment from @Era actually displays this. When we are talking about a particular tire on the specific car, thus referring to a definitive, well-defined object, Era uses the apostrophe-s construction:
My car's front left tire.
But when @Era talks about a not-individually-defined door (the car could have one, but most have at least two, if not four or more), now referring to an indefinite object, the apostrophe-s construction is dropped.
My car door.
@user3169 brings up the idea that possession isn't necessarily involved with respect to car door or computer monitor. A door can exist without ever being part of a car, and a monitor can exist without being part of a computer. Thus these adjectives do not add possession because they don't clearly define the object as belonging to (or in other words, as being possessed by) a specific object.
This doesn't mean they can't. Defining the tire as being THE front left tire of the car (as opposed to any old tire) assigns possession of that specific object to another specific object (This is my car. There are many like it, but this one is mine.)
Generally speaking: if the object is indefinite (just any old X), it doesn't use the apostrophe; if the object is definite (not just any X, my X), it uses the apostrophe. Exceptions abound (this is English, after all) but it's a good rule of thumb.