Eli5: How is the speed of a rotating object defined (e.g. a windmill) if you don‘t use rpm. Where do you measure the speed in mph?

Question

I had a look at a huge windmill and was wondering how fast the blades are spinning. Obviously, the distance the blades make is different on the outside than on the inside. Is the speed of a rotating object always measured in rpm and not in mph?

In: 3

Answer 1

The tangential speed of something moving at an angular speed of w at a given point that is a distance r away from the center is v = wr.

So for example, a windmill spinning at 10rpm = 20pi rad/min would have a tangential speed of 100pi feet per minute = 3.6mph at a distance of 5 feet from the center (v = 10rpm x 2pi rad / rev x 5 feet = 100pi feet per minute).