1

Shut up you idiot!

Shut up idiot!

How does "you" affect the meaning of the first clause? Are they both formal ways of addressing?

2

This is direct address in both cases, although it is hardly formal, so there should be a comma after "up" if this is in writing:

Shut up, you idiot!

Shut up, idiot!

There is no significant change in meaning.

This is not a polite usage.

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