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First of all, frequency and angle have different physical dimensions.

'Frequency' has a reciprocal time in it ... "per second" ... and angle doesn't.

The relationship you really want is the one between frequency and angular frequency ...

"revolutions per second" and "radians per second".

1 revolution = 2 pi radians

1 revolution per second = 2 pi radians per second

1 revolution per year = 2 pi radians per year

Angular frequency in radians per second = (2 pi) times (plain old frequency in Hz)

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Q: What is the relationship between frequency measured in Hz and angle measured in radians?
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