I was wondering; what exactly is the difference between kinetic energy and momentum? I was just thinking about this the other day, and I couldn't quite work it out. I'm not talking in definition-wise terms; I know that momentum=mv and kinetic energy=1/2 mv^2, and can see that the derivative of kinetic energy with respect to v gives you momentum. My question is, what exactly is the physical relationship between these two, for lack of a better term, attributes of an object in motion. Like, what does squaring the velocity actually do to differentiate the two? I'm actually not too sure what it is I'm looking for, all I know is I haven't figured it out satisfactorally yet :P. I guess I'm just looking for the conceptual difference between them.