The title says it all and I just wanna know the stuff behind how it is and how it works!
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There are two sides to this question.
One of them is the kinematics – how things move, completely ignoring the physics. If you trace out a circle, and trace a larger circle around it in the same amount of time, you must have been moving your pencil faster to trace the second circle. This is a consequence of geometry – if we want to the pole to continue being a pole, and for all of it to be rotating at the same number of revolutions per second, the far end of the pole must be moving faster, because it’s tracing a larger circle.
The other side is dynamics – how does the pole ‘know’ to keep the middle bits moving slowly, but to make the outside bits move quickly? The answer here is that the molecular structure inside the pole has a preferred configuration. If you try to move the molecules farther apart from each other, they will pull on each other harder to get back together – in an analogous way to how rubber bands have a preferred size, and if you stretch them they will have a reverse force that gets stronger the farther you stretch. So initially, the pole actually doesn’t know that the outside needs to move faster than the inside. You just apply a force to the pole to get a single part of it moving. The molecules around your point of contact want to stay in the same place, but there are now molecules that are moving because of your hand, and after some internal stretching, compressing, and other shifts, all the molecules start to move in tandem. The outside of the pole doesn’t yet know that this has happened, and is getting left quite far behind – and again analogously to a rubber band, this result in an even larger force, which gets the outside of the pole moving much faster than the part you were accelerating with your hands.
You can see this process on a slow-motion video. When long enough rigid object starts to rotate, you can see that close to the points you apply pressure it responds quite naturally, but the farther you get from that the longer the delay until motion starts, and the more dramatic the deformity is as the pole is getting up to speed.
So the pole doesn’t ever need to know anything, it’s always just atoms and molecules pushing or pulling on each other, and in rigid objects instead of keeping track of all the individual particles we can make a simplifying assumption (almost 0 deformation), which results in a much simpler description of the motion (speed proportional to the distance from the axis of rotation).
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