24. You can think of it in terms of how hard it would be to rotate the spindle if the weights are near the center vs. if they are toward the edges. When they are near the center, it's easier to rotate. You can relate this to how it's easier to lift a sledgehammer with arms outstretched if you hold it by the heavy end compared to if you hold it the other way around. The hanging weight is a constant force, so it'll accelerate down less if it's trying to turn the spindle with the weights on the edges. I don't think an equation would be useful here so much as just a fundamental understanding that it's easier to move something when the weight is concentrated toward the center as opposed to when the weight is toward the edge.
25. This just has to do with center of mass. You can try taking it to an extreme. If the spindle and the weights are 100ft above the base, then a weight pulling on one side could easily topple the whole apparatus.
Again, probably not very helpful to invoke an equation here. Better to just try to understand intuitively that shifting the center of mass around like that will make it less stable.
26. As you increase R, it's basically like you're increasing the level arm for the string attached to the hanging weight. That means that for the same amount of force you get more torque. Easier to rotate the spindle, therefore less "resistance." As for the mass travelling farther per revolution, that's just because the spindle wheel has a larger diameter, so the circumference is greater.
