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This question already has an answer here:

I have been driving myself mad trying to prove it one way or the other, I understand how it is derived and how to use it etc. but it still seems to me to be saying that (m/s)=(rad/s)*(m) which I don't think is dimensionally homogenous, what happens to the radians. Couldn't find anything on the internet about the homogenuity of it. I am probably just being stupid but please if anyone could shed some light on this that would be amazing.

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marked as duplicate by Aaron Stevens, By Symmetry, Community Mar 7 at 14:32

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What you call angular rotation is angular velocity. The dimension of angular velocity is one over time, because the angle is dimensionless.

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  • $\begingroup$ hyperphysics.phy-astr.gsu.edu/hbase/rotq.html I was just on this site and they said the angular velocity has the units radians/second, in the bit about angular velocity. Also I always thought that angular velocity=2*pi*f where f was rev/s. Am still a bit confused. Thanks for the speedy answer though. $\endgroup$ – Dean Magnus Mar 7 at 14:26

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