I was driving the other day and couldn't help but look at all the wind mills in the wind farms. I know I am not doing the math correctly, but I want to know what is "really" happening when a windmill spins.
Suppose there is a wind mill with one blade that is 1 foot long. Now lets say it takes 1 second to complete a rotation. It travels in a circle. We can calculate the circumference of this circle by 2*R*PI => 2*1*PI which leads me to believe that the blade is traveling 2*PI feet per second.
But now let us take an arbitrary point on the blade, say .5. Now the circumference is 2*.5*PI which would then make the speed PI feet per second.
To me this means that different parts of the blade are traveling at different speeds, but intuitively this is not possible. Where is my logic wrong? I am more of a math guy, but I was very curious about this question and wanted to see the physics point of view.