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 one thing I actually learned from being a laserdisc geek. Those come in two varieties, CLV and CAV.
CLV = Constant linear velocity – in other words, the linear speed of the disc is constant, so in your example of 10km/h, every point along the disc would be going at that speed. This doesn’t make sense for a windmill, though, it’s meant for something that’s read at a specific point, like a disc.
CAV = constant angular velocity. This is the far more common one, your windmill example would be CAV as are vinyl records. This means the rotational speed is constant, and the inside of the disc is traveling faster than the outside. Think of a 33 or 45 RPM record, it’ll gradually appear to be spinning faster as it gets closer to the center even though the turntable is going at a constant speed. This is also why they measure it in RPM, since the speed will vary based on where you measure it.
CLV is a lot less common of a system and only really used for laserdiscs and magnetic media like floppy disks where every sector needs to be an identical size. If you were to watch one of those play, it would make the motor spin faster and faster as it made its way out (or slower and slower as it made its way in) to keep that linear speed constant.
This is mostly off topic, but basically anything with rotational force has two different ways it can operate. You either have the outside of the spinning object (a disc, or rotor blades, etc.) going slower than the inside, or you vary the rotational speed as you’re measuring/reading/writing to a specific point
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.
You are correct. The tip of the fan blade must move faster than the midpoint (I assume that’s what your phrase “the point furthest in the middle” means), which moves faster than the part of the blade closest to the hub.
This is the difference between *linear* speed and *angular* speed. One is total change in location, the other is total change in *angle.*
All parts of the windmill blade except the absolute center point have the same *angular* speed, because “angular speed” is measured in degrees changed per second (or, more commonly, “radians” per second, which makes the math simpler). But because one radian means more *distance* the longer the circle’s radius is, yes, something very very long will be moving *linearly* faster at the outer edge of its rotation than something very short.
Latest Answers