I have a real-world problem that I'm quite certain can be solved with a formula. Unfortunately I myself am not particularly skilled in the realm of physics or math. Any and all help is very much appreciated!
I have a cassette tape. It's on a transport that does not use a capstan to drive the tape. As the tape travels from the first reel to the second, the first reels diameter decreases while the second reels diameter increases as the tape moves from one to the next.
In this situation, both reels have independent speed control. At what rate does motor A need to increase/decrease in speed, in proportion to motor B, to maintain constant speed and tension on the tape between the two reels?
I want to calculate the velocity from the radius. To know the radius, we have to know where we are on the tape.
Any ideas on the best way to go about this?