nagen
to gnaw
To repeatedly scrape at something hard with the teeth or bite off small pieces of it, as is typical for rodents.
Die Maus nagt ein Loch in die Holzwand.
The mouse gnaws a hole in the wooden wall.

to gnaw
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to gnaw
To repeatedly scrape at something hard with the teeth or bite off small pieces of it, as is typical for rodents.
Die Maus nagt ein Loch in die Holzwand.
The mouse gnaws a hole in the wooden wall.

The verb 'nagen' (to gnaw) is almost always used with the preposition 'an' and the dative. This applies to both the literal and the figurative meaning.
Der Hund nagt an einem alten Knochen.
The dog gnaws on an old bone.
The verb 'nagen' (to gnaw) is the base word for the noun 'der Nager' (the rodent). It describes the typical action of this animal.
Man hört, wie die Mäuse auf dem Dachboden nagen.
You can hear the mice gnawing in the attic.
You can tell whether 'nagen' (to gnaw) is meant literally or figuratively from the subject. If the subject is an animal, it is literal. If the subject is a feeling or an abstract idea (e.g., doubt, hunger, conscience), it is meant figuratively.
Der Biber nagt an einem Baumstamm.
The beaver gnaws on a tree trunk.
In the figurative meaning, 'nagen' (to gnaw) is often connected with negative feelings and states. Typical subjects are 'der Zweifel' (doubt), 'die Sorge' (worry), 'das Gewissen' (conscience), or 'der Hunger' (hunger).
Die Sorge um ihre Zukunft nagt an den Studenten.
Worry about their future gnaws at the students.
The idiom 'am Hungertuch nagen' is a fixed unit. It means to be very poor and is always used in this form.
In den Kriegsjahren mussten viele Menschen am Hungertuch nagen.
During the war years, many people had to live in extreme poverty.
to torment / to struggle
'quälen' and 'nagen' can both describe inner unrest or worries. 'quälen' directly says that something places a heavy burden on someone. 'nagen' is more figurative: a feeling or doubt slowly keeps working on someone and does not let them go. Typical phrases are 'Zweifel nagen an jemandem' (doubts gnaw at someone) or 'Sorgen nagen an jemandem' (worries gnaw at someone). When the burden is strong and directly in focus, 'quälen' fits. When it works quietly but persistently, 'nagen' sounds more natural.

Seit der Absage nagen Zweifel an Max, obwohl er sich gut vorbereitet hatte.
Since the rejection, doubts have been gnawing at Max, even though he had prepared well.
Nach dem Streit quälte sie der Gedanke, ihre Freundin verletzt zu haben.
After the argument, she was tormented by the thought that she had hurt her friend.