I saw a video of a windmill a few minutes ago and they are quite fast.
But then i thought “Is the tip of the rotorblade as fast as the the point furthest in the middle?”
Let me explain the best i can:
So if you move 10km/h, after 1h you are 10km farther than before. Thats logical.
But with regards to the rotor blade, the point furthest in the middle moves less far than the one all the way outside.
Does that mean that the points move at different speeds even though they’re part of the same body?
Where is my mistake in thinking?
In: Engineering
This is in fact correct, if you think about it linearly. The linear velocity changes at each point along the blades. The centre of the turbine shaft isn’t moving in a circle, the tip of each blade moves at velocity v. Every point between there moves at some fraction of v equal to its location as a fraction of the radius.
However, if you express the velocity of the windmill as _angular_ velocity, ie the radians per second of rotation, or more simply, the RPM of the blades, then every point on the blades travels the same fraction of a circle every second, whether it’s at the tip or in the middle of the turbine shaft, or even somewhere partway along the blade. If the turbine rotates at, say, 60 rpm, it has an angular velocity of τ radians per second, or 2π rad/s, or 360°/s.
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