# Circular motion normal force

Some roller-coasters have loop-the-loop sections, where you travel in a vertical circle, so that you're upside-down at the top. To do this without falling off the track, you have to be traveling at least a particular minimum speed at the top. The critical factor in determining whether you make it completely around is the normal force; if the track has to exert a downward normal force at the top of the track to keep you moving in a circle, you're fine, but if the normal force drops to zero you're in trouble.

I've been told the normal force is a contrapositive force. I mean, when I'm at the top of the loop, the weight already points down so how can there be a normal force, if I'm not exerting a force to the road?

When you are on the top of the rollercoast loop the following forces are acting:

• weight force $mg$ pointing down;

• centrifugal force $F_{centrifugal}$ due to the velocity you have in circular motion that points up;

• normal force $F_n$ that rails exert on the cart that points down;

Apply 2nd Newton Law and find that:

$$F_{centrifugal} - mg - F_n = 0$$

In particular if $F_{centrifugal} > mg$ then $F_n \not= 0$ and positive.

Note that $F_{centrifugal}$ direction is up and not down because you are not in inertial system frame.