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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.

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  • $\begingroup$ The radian has a very precise and well defined meaning in mathematics. It's a lot more than a label. Degrees are simply a human convenience and we've used many different units for human purposes (e.g. a gradian) but none work in the same fundamental way that radians do for mathematics. $\endgroup$
    – StephenG - Help Ukraine
    Commented Aug 12, 2017 at 13:14
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    $\begingroup$ I recently had an interesting discussion about Hertz. A document used Hz for frequency and rad/s for angular frequency. After some thought, we all kind-of agreed that using Hz for angular frequency (without a clear statement that it is angular frequency) is not a good idea. Hz is too strongly associated with frequency in our general opinion. $\endgroup$
    – garyp
    Commented Aug 12, 2017 at 13:15
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    $\begingroup$ @StephenG No disagreement on the importance of radians in mathematics but the OP has a point. It doesn't need a unit in the way that velocity or area do. If we had not got into the habit of using degrees before realising that maths worked better in radians, we might not have felt the need fid the name. We would just say that the angle was $\frac{\pi}{2}$. $\endgroup$
    – badjohn
    Commented Aug 12, 2017 at 13:22

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