Here's where Steph explains what radians are. So let's talk about angular speed.
The important thing to remember about doing anything angular is that you can always find an analogous linear concept to help you. In our case, we recall that in everyday life,
Okay. So if we want to think about angular speed instead, we're going to have to convert every one of these quantities to an angular one. Time is just time everywhere, so we're okay. But when you're thinking angularly, you don't care about how far you go (the distance) -- you care about how many angles you've turned. That is, the analogue of distance is angle!
So if we knew, say, that a wheel turned through six radians in a second, then our angular speed would just be 6 rad/s. See, it's not any more complicated than our normal concept of speed.
Oh, and a note about conversion: sometimes you might get an angle in degrees (in which case the linked post tells you how to convert in between them), and other times you might get an angular speed in rotations per [unit of time]. In that case, just remember that one full rotation is 2π radians for any circular object, so you can use that as a conversion factor instead.
Hope that helped!
- H2
