For determining the COF, you'll want to test a SINGLE paper-to-paper contact surface. All mass above the contact surface will contribute to the normal force. I'd use maybe a notebook to press the contact surfaces together. Or you can use a laboratory mass. You don't want to go too heavy...
In circuits, it's fairly easy to visualize electrons pushing on one another. Voltage is a potential for a charged particle to move between two points. Electro Motive Force (voltage). For a phenomenon that's physically analogous in circuits, maybe the concept of pressure?
That does sort of...
For crutches, I wouldn't think that spring rate, per se, is a concern as the impacts will be fairly evenly spaced and much farther apart. You just don't want it to rebound too quickly or they'd turn into pogo sticks. Probably going to be a tradeoff between building in enough travel/cushion to...
For mathematics? Repetition. Devoting 2-5 hours daily to working textbook problems. I was lucky enough to attend a school where I had access to calculus professors several hours a day. Their offices adjoined the math study room where I've basically lived for the past 2-1/2 years, and having...
the best way to determine COF would be to use a single contact surface (paper to paper), with a known mass pushing down on them. Determine how much force it takes to cause slip, divide by the normal force (mg), and that will yield your static COF. Repeat several times.
You could then vary the...
The pulley is a very good idea. If the height of the pulley (and the attachment to the force meter) are such that the tensions are perfectly horizontal, then your normal forces will be more correct. I wouldn't assume a COF, or that it would not vary with surface area (see previous comment)...
Go polar?
Depending on what your velocity function looks like, you'll probably want to convert to polar coordinates, as it makes it easier to find the rate at which θ is changing as the turret tracks the target. r(t) and θ(t) Or just work it out as a triangle using law of sines/cosines...
If the books are unsupported, and in the vertical position, it will be quite difficult to ascertain the normal forces. And indeed, the normal force would probably only be able to be determined indirectly and even then only if the coefficient of friction between the contact surfaces is...