The man wants to practice so that he can bear a force equal to that due 3.6 times the force due to gravity. If the mass of the man is m, the force he wants to withstand is 3.6*g*m = 35.28*m N
He uses a centrifuge to practice. The centrifuge has a radius of 10 m; let the speed it has to rotate at so that the astronaut is expelled outwards with the required force be v.
This gives m*v^2/r = 35.28*m
=> v^2 = 35.28*10
=> v^2 = 352.8
=> v = 18.78
W = v/r = 1.878 rad/seconds
The angular speed of the centrifuge should be 1.878 rad/s