Murdoc88 said:
Is a proportionality statement something (alpha) something when written in proper notation and from there I could derive an equation by use of a constant? I just don't really know what to write.
I just have a few points about that
1. Yes, what you have described is what a proportionality statement *looks like*, although not necessarily what it means. Note also that you have described a mathematical statement of proportionality, whereas your assignment just asked for one in words.
2. This is just a nitpick, but the symbol for "proportional to" isn't the same as the greek letter alpha:
\textrm{alpha} \rightarrow \ \alpha \ \textrm{vs.} \propto \ \leftarrow \textrm{proportional to}
3. Getting back to what it means, I think you probably have an intuitive sense of what it means when we say that something is proportional to something else. Take force and acceleration. When we say that force and acceleration are proportional, we mean that the larger the force, the larger the acceleration, the smaller the force, the smaller the acceleration. As one increases or decreases, so too does the other. If one changes by a certain
proportion, then the other changes by the
same proportion. If you double the force, you double the acceleration. In other words, from all of this, we can deduce that the statement "the acceleration of an object is directly proportional to the net force acting on it" really boils down to a statement that there is a
linear relationship between the two quantities. If x did
not vary linearly with y, but quadratically, or in some other way, then x would NOT be proportional to y. It would be proportional, however, to y^2 (or whatever).
4. What about the so-called "constant of proportionality?" Mathematically, of course, you can't equate a force to an acceleration, since they are two different quantities with two different dimensions. So you need the constant there as a sort of conversion factor. But that doesn't offer much insight. A more intuitive physical interpretation of this "conversion factor" is
how much acceleration you get per unit of force, how many m/s^2 you'll get per Newton. Therefore, we can conclude that the mass of an object is a measure of how hard it is to change its state of motion (to accelerate it), since the more massive an object, the less acceleration you get for the same force (the less bang for your buck a \propto \frac{F}{m}). In Newtonian mechanics, this is a good operational definition of mass (inertial mass, anyway). I cite this example because it was the first "constant of proportionality" that took on a real physical meaning for me, and illustrated the usefulness of determining the relationships between quantities. I hope that this will help you understand what it is that you need to state about the centripetal force and the frequency.
