This question may seem simple, but I have no idea where to start.
I'm in design phase of a hobby electronics project and need your help. Basically, I'm going to have two platforms with electronics on both of them. I'm planning to have a stepper motor on the bottom platform which will be connected to top platform by an axle. I plan to use a microcontroller to precisely control the intensity of angular velocity of the motor and the angle by which it will rotate. I will also need to use wires to connect the bottom platform to the top platform. My idea is to have wires run on the outside of the axle and be long enough that the axle will be able to rotate by some angle of $±θ$. In normal operation the angle shouldn't be grater than 2π, so I want to avoid constructing some complex mechanism which will transfer current irrelevant of the axle's rotation.
Image (I apologize for my bad drawing skills) shows the two states which are interesting (at least in my opinion) here. The top is when the axle is in neutral position and angle by which it is rotated is 0. While the image does not show it, the wire will be loose. The bottom image shows what I expect will happen after the axle has been rotated by a certain angle.
The two black rectangles are soldering joints by which the cable will be connected to the bottom and the top platforms. The red line is wire.
Here's direct link to the image. It is more clear there.
Here's my question: Is I have an axle with length L and radius R, how would I calculate length l of a cable running form the top of the axle to the bottom after axle has rotated by a certain angle θ?
Also, I have no idea which tags would be appropriate, so do feel free to edit them.