Question

Uranium enrichment centrifuges spin very fast. If a centrifuge is 60 cm in diameter, and spins at 64,000 rpm (these are real estimates for modern enrichment centrifuges; exact specifications are classified), what is the centripetal acceleration experienced by the wall of the centrifuge in terms of the acceleration due to earth’s gravity (9.81 m/s2 )?

Answer 1

Given d= 60 cm = 60*10^-2 m, R = 30*10^-2 m

         W = 64000*2*3.14/60 = 6698.67 rad/s

cnetripetal force F = mv^2/ R = ma

centripetal acceleration a = v^2/R,    here V= R*W

                                              = R^2*W^2/R

                                              = R*W^2

                                             =30*10^-2*6698.67^2

                                               = 13461653.93 m/s^2

                                               = 1372237.91g m/s^2