Initial explanation of "why the roller coaster doesn't fall off" is poor. In fact, the explanation doesn't even mention gravity, which is odd, because if the coaster were to fall off gravity would presumably be the force responsible. The author explains that the track is applying a downward force on the inverted coaster: but that force would surely combine with gravity to accelerate the coaster downwards, which is the opposite of the apparently observed phenomenon we're trying to explain here. Of course that -is- what happens, but only because the coaster is going fast enough that gravitational acceleration downward would curve the cars down less than the track does.<p>The trick is to realize that an unguided rollercoaster, not on a track, wants to travel along a parabola (not in a straight line, as indicated in the text). If the coaster is going fast enough, then the radius of curvature of the parabola at that location in the coaster's trajectory is greater than that of the track, in which case the track gets to apply additional centripetal force and turn the coaster -more- than it 'wants' to. If the coaster is going slow, then the radius of curvature of the parabola will be less than the radius of the track, and the natural path of the coaster will tend to pull it down away from the track.<p>Of course, at that point, you find out what -really- stops the coaster from falling off, which is that it's riding on a tubular steel track with wheels clamped both above and below the rail...<p>All of which is mentioned - later in the article, but as an introductory section, messing up the basics so badly really undermines the article.