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The radian is defined as the ratio of the circumference and the radius. Both are measured in meters. So there should not be a unit for that. But we use 'rad' as the unit of the radian value.

The coefficient of static/kinetic friction also the same, it is a ratio of both forces. Therefore it doesn't have a unit.

So, is there a special reason to have a unit for the radian value?

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Probably just to emphasise that you are not using degrees. If we had never used degrees then we might not feel the need to say radians.

There are other unnecessary units e.g. becquerel and hertz.

badjohn
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