What causes (the feeling of) lateral force on roller coasters?

Answer 1

It's because of your Inertia. Anything with mass has inertia (reluctance to move).
So in the roller coaster, you are going in one direction at a constant speed and your body is fine with that. Since there's no change in direction or speed so no inertial forces.
But when there's a sudden change in direction for example, your body wants to continue in its original path (straight) but you are forced right say, hence you feel as if theres a force pushing you to the side.

Answer 2

saj is correct. Here is the reason in math talk if that appeals to you.

Momentum is a measure of inertia...momentum = p = mv; where m is your mass on the roller coaster and v is your velocity wrt the ground. Now, your roller coaster car takes a sudden turn. In which case, your velocity changes because velocity is a vector consisting of both magnitude (speed) and direction. When the car turned, it changed direction; so there was a change in velocity during the time it took to make that turn, which can be written as dv/dt. dv means change in velocity and dt means change in time.

OK, then mv becomes mdv/dt because of that change in velocity. And p becomes dp/dt because of that velocity change. So p = mv becomes dp/dt = mdv/dt = ma = f where dv/dt = a = acceleration.

So there we have it, f = ma, one of Newton's famous laws of motion; where f = dp/dt is often called net force. For your question, we can call it "lateral force", but it can be force in any direction depending on which direction v changes.

Answer 3

inertia?