Thoughts on climbing

I have always thought that momentum is a bikers best friend. It is especially true in mountain biking where being able to see ahead, read the trail and pick the right line means a smoother faster ride with less energy spent. I used to love it when I was gaining on another rider while he was pedaling and I wasn't. I often thought that if I rode well on a particular day my time spent pedaling would be less than any of the other riders. This in turn would leave me with more energy for climbs and riding the more technical sections of a trail. I have always said "speed is your friend" for technical sections which simply means if you can have good forward momentum and hit the right line you will like flow over rocks and roots instead of bogging down like a slower rider would.
After road riding for a few years now I am discovering that there is a lot to be said for momentum on the pavement as well. In particular I am learning some climbing techniques which I think work well for me on smaller climbs and now seem to apply on longer climbs as well.
In the last year I have noticed that on smaller climbs such as what you would find in an area with rolling hills if I keep my speed up starting the climb and work on keeping my cadence up, possibly shifting to a lower gear once or twice on the way up, I arrive at the top faster while at the same time spending less energy. It seems to me many riders don't attack these smaller climbs and therefore end up "hammering" up the hill with a low cadence resulting in their spending more energy to arrive at the top of the hill in a slower time. My idea is if you can keep your momentum at the bottom half of the climb the top half will be easier and faster to complete.
I am now learning that momentum is also your friend on the much longer climbs but in a much more subtle way. It seems the faster you can climb up a hill the more that momentum aids in gaining even more speed. Think about it. If you are riding up a hill doing 13 kph while Joe Biker is doing 20 kph his bike is traveling slightly farther every pedal stroke he takes because the momentum he has created. Certainly the fact that he is stronger and in better shape than me has a great deal to do with it but I don't think it is a 1:1 ratio where because he goes up the hill 50% faster he is 50% stronger and in better shape than I am. I have no doubt an equation could be created which which could explain mathematically the science of climbing regarding energy spent, power used and momentum created to achieve maximum speed.
Or it's entirely possible I am completely full of shit.