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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$\begingroup$ Radians are dimensionless. Technically you have $m/s=(1/s)\cdot m$ $\endgroup$– BioPhysicistCommented Mar 7, 2019 at 14:24
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2$\begingroup$ Possible duplicate of Question about Radian as a unit $\endgroup$– BioPhysicistCommented Mar 7, 2019 at 14:25
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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. $\endgroup$ Commented Mar 7, 2019 at 14:26