Curving on a flat track and on a banked track
Regardless of whether you curve on a track in roller derby or on a motorway in NASCAR: if the track is banked, curving is easier than on a flat track and you can go faster. The reason lies in the circular force.
First, we will look at a curve in general. This applies to any sort of curve, regardless of whether it's on a flat track, a banked track, or even a curve on a street.
Forces at curves
If you are curving, you experience a centrifugal force which pushes you to the outside of the curve. If you are too fast, you may even fly out of the curve. However, people looking at you and standing still don't experience the force as you feel it. The centrifugal force can only be experienced by you because you are the one moving into the curve. Looking from the outside, you don't actually see the centrifugal force. To be accurate, what you see when the skater curves instead of going straight is called the centripetal force. From the point of view of physics, the centripetal force provides a more sophisticated way for describing the motion. The centripetal force is the actual force which drives the skater into the curve as opposed to just going straight forward. But describing the motion from the skater's point of view, the centrifugal force can be used as well. The centripetal force is exactly as big as the centrifugal force.
The smaller the curve's radius, or the faster you take the curve, the stronger the centrifugal force is. In order to stay in the curve in sports like roller derby or speed skating, your muscles have to build up a sideways force to compensate for the centrifugal force. If you curve with a car, then the wheels have to build up this force.
The centrifugal force is the reason why athletes doing laps in any kind of sports don't necessarily go the shortest way in the inner lane of the curve. Instead, sometimes they go towards the outer lanes when they curve. This makes the curve's radius bigger, which makes the centrifugal force smaller. Therefore, it is easier to curve. The disadvantage of the longer path is more than compensated for through the smaller centrifugal force.
Now we can look at a banked track curve.
The banked track curve
Here, we have a helping force from the ground, which pushes against the centrifugal force. Any surface will bear a counter force to a force pushing against it. The first time I heard about that, I found it quite strange. An inanimate object can bear a force? Yes, it can, and it doesn't need any energy to do so. You can easily experience this for yourself by pushing against a table with your finger. What do you feel? That's the force from the table pushing back at your finger.
The surface's or the ground's force is exactly perpendicular to it's surface. In physics, this force is called the normal force. And because the ground is tilted on a banked track, this force points partly against the centrifugal force and thus compensates for some of it (see figure above). This is very helpful because the athlete's muscles have to build up a smaller sideways force to compensate for the centrifugal force. Thus, it is easier to curve on a banked track than on a flat track.
If you look at freeways, you can actually see that curves are slightly banked as well in order to decrease the centrifugal force. Driving through curves becomes safer this way.
