Question

How does momentum and impulse affect roller coasters?

Answer 1

In simple terms, momentum is the measure of mass in motion, ie. how much amount of mass is in how much motion. Impulse on the other hand is the overall effect of a force acting over time. Impulse is equivalent to a change of momentum. Because of this relation, there is a direct connection between a force that acts on an object over time and the motion itself. So, a roller coaster moving at a high speed has a lot of momentum.
Since momentum is velocity * mass, the velocity needed at the bottom of the roller coaster to make it all the way up to the top of the loop is independent of the mass.
Thus, the more the momentum on the roller coaster, the harder it is to stop it or change its direction.