# eli5 why does a poll spin faster the farther it is from the center?

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The title says it all and I just wanna know the stuff behind how it is and how it works!

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every part of the pole travels the full circle during the same period of time.

but points further away from the center travel in a circle with larger radius, the the distance they travel during the full circle is greater.

more distance over same time means higher speed.

So there are two ways of measuring how fast something is spinning.

First is how many revolutions a second it is making, if it takes 1 second for the pole to spin all the way around to its original position, then it is spinning at 1 revolution per second, across the entire pole no matter how far from the center.

Or you can measure the actual velocity of a specific point on the pole traveling the distance.

Since the whole pole is spinning at the same rate in revolutions, the parts towards the outer edge travel faster during that 1 revolution, because they have more distance to cover in their circle. Imagine you mark 3 points on the pole, 1 close to the center, 1 halfway to the edge, and 1 at the edge. When you spin the pole all three create a circle, but the point towards the outer edge creates a much much bigger circle.

Since it is traveling around a bigger circle in the same amount of time, it must be traveling faster.

the short answer is “it’s got farther to go” you can work it out in a few steps.

1.) if the pole is spinning it’s all turning together because it’s a solid object, right? when the middle bit makes 1 full rotation the outer bit has to as well.

2.) the outer bit has to go all the way around in a big circle in the same amount of time that the inner bit just has to turn a much smaller circle, so the outer bit must be moving very fast to do that.

I think the part that seems weird is when you say the pole is one solid object, you want to say that one part can’t move faster than another part, right? it would tear itself apart. but that’s just the funny thing about rotational motion, the actual speed does depend on how far you are from the center.

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).