Definition:Minute/Linguistic Note

Linguistic Note on Minute
The word minute, in the context of the measurement both of time and of angle, derives from its initial definition as a minute part of an hour or of a degree of arc.

In this context the word minute (meaning: the aggregation of $60$ seconds) is pronounced min-it.

The word minute (as used in the phrase minute part) is pronounced my-nyoot and means small.

So the fact that the two words are spelt identically is not a coincidence.