Centripetal Acceleration and its effects
The only known (and possible) method for achieving artificial gravity is through the force of a centrifuge. Centripetal acceleration is calculated from the following equation:
[a] = centripetal acceleration
The only significant experience with gravity other than 1G was with the Apollo astronauts on the moon. Even so, the duration of those missions (about 10 days) was not long enough to have any significant affects. We then assume that the crew of the Mars mission must have an artificial gravity of 1-G. (that of Earth).
Effects of rotation
In the 1960s the U.S. Naval School of Aviation Medicine in Pensacola, FL organized a series of experiments where test subjects lived in a rotating room for weeks. At 6 rpm practically every subject showed signs of motion sickness. At 2 rpm and below, only mild symptoms were experienced by few, even those highly susceptible to motion sickness. Eventually the subjects showed increased tolerance to the higher rates, but a corresponding period of readaptation was required.
During the Mars mission this period of readaptation could occur during the atmospheric entry and rendezvous. However, the value of 2 rpm would exclude only a small fraction of the populace and require a negligible readaptation period.
Substituting the values of 1-g. (9.8 m/s^2) and 2 rpm (0.2094 rad/s) into the above equation gives us the required radius of 223 m.