Banked Curves and Centrifuges

To keep an object moving in uniform circular motion, something must exert a centripetal force on it. In the case of cars driving around a race track, that centripetal force must come from the roadway surface.
If the roadway is flat, then friction between the tires and the road must supply all the centripetal force.
But if the roadway is banked, then some of the normal force from the roadway can supply all (or some) of the needed centripetal force.

One can derive the bank angle theta which is just right for cars driving at speed v around a track of radius r:

                              v^2
              theta = atan ( ----- )
                              g*r

Centrifuges spin liquids at very high speeds around and around; they can place very strong centripetal forces on the liquids.

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