All the circular motion featured here have very similar dynamics.
(1) Conical Pendulum
(2) Flying Chairs
(3) Airplane turning a horizontal circle
(4) Cars turning on banked curve
NASCAR race cars do not slow down when they turn. The tracks are banked (slanted) at the bends. Banking allows the cars to utilize the normal contact force that the track surface exerts on the cars to help provide the required centripetal force. This allows NASCAR to turn at full speed. In fact, at particular speed and angles, the cars can negotiate the bends without the tires providing any sideway frictional force at all. The following video explains.