Roller coasters actually have a lot to do with science, especially physics. The most prominent way roller coasters relate to science has to do with gravitational potential energy (GPE) and kinetic...
The science behind roller coasters is pretty simple. They actually go waaay back in history. Now at days, people use steel or metal to build it. They bolt it together and viola! A Roller Coaster! But...
The momentum it takes to keep them going. Most only use gears and such to get you up to the top, which is why it's usually the highest drop. After that, it's all gravity.