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Is there any difference between nagen and annagen?
They both mean to eat away at something., like a mouse or a cat would do.
What is it that the prefix an- does to the verb? Does it add any special meaning?
Knowing that in case would maybe help me to remember better.
First of all nagen is just the verb/the activity, without specifying what you're eating away from. Annagen must have a target: etwas annagen (eating away at something).
Also the an- can mean that you just begin to do it but don't even remotely finish.
For example etwas anarbeiten means to start working on something without finishing it (arbeiten = to work).
The opposite of the an- would in most cases be ab-.
For example einen Knochen abnagen means that afterwards there is nothing left on it or alles abarbeiten means to process everything until there is no work left to do.
You have always "nagen" + "an", just in two different combinations in order to stress different aspects.
"Nagen an" emphasizes the activity as such and its cause, even if you can't grasp it:
Irgendetwas nagt an ihr, aber sie will uns nicht sagen, was es ist.
Diese Maus nagt jetzt schon zwei Wochen lang jede Nacht an irgendetwas herum.
"Annagen" emphasizes what is being eaten away:
Ihr Hund hat schon wieder meine neuen Schuhe angenagt!
