This question pertains to the notion of constructing rotating spacecraft and habs for human use in space in order to mitigate the effects of microgravity. Such craft have been a staple of many sci-fi works and pop films, but no craft to date has employed this on at least a serious scale.
The basic concept is to imagine two capsules at the ends of a long cable or, perhaps, if one really wants to make it expensive, a giant ring, like a wheel, rotating about a central axis. The setup rotates so that the apparent force vectors along the cable / out from the wheel center, are enough to provide "good" gravitational conditions - about one gee, ideally - inside the habitation.
The size of the needed habitation can be found from elementary mechanics: if the desired acceleration is $a$, then the criterion for the rotation is
$$a = \frac{v^2}{r}$$
where $r$ is the ring radius and $v$ the velocity at the rim. If rotation is measured in angular velocity $\omega$ instead, then, $v = r\omega$ and
$$a = r\omega^2$$
Taking $a$ to be $9.8\ \mathrm{m/s^2}$ and $r = 5\ \mathrm{m}$ shows that for a ring with 5 m radius (10 m diameter), you need an angular velocity of 1.4 rad/s, or 0.22 rev/s (one revolution every 4.5 s). This is a respectable velocity, commanding a decent amount of rotational kick (kinetic energy), but not impossible.
However, an interesting problem with a tight ring seems to be the following: note that from the formula just given, there is a very obvious dependence on $r$ for any given rotational speed $\omega$. This means that, within the rotating reference frame established by the rotating spacecraft, there is a gradient of force depending on the distance from the center, and that means also a gradient of force over any extended object, such as a human, within that craft. In particular, the figures above assume a point object, but a human is extended, perhaps considerably, e.g. a guesstimate for the world average figure (remarkably hard to find, just a guesstimate of such from a long time ago) is 1.70 m height.
The force gradient between two points is easily seen to be in fact even independent of the size of the ring: it is
$$\Delta a(\Delta r, \omega) := (\Delta r)\omega^2$$
and thus solely a function of the "height" of the human $\Delta r$, and their rate of rotation, $\omega$. Of course, a larger ring can rotate more slowly to produce a given "gravity": twice the radius, and you quarter $\omega$. Taking the above figures with $\Delta r := 1.70\ \mathrm{m}$, $\omega := 1.4\ \mathrm{rad/s}$ gives a $\Delta a$ of about 3.3 $\mathrm{m/s^2}$, which seems like a VERY significant delta-gravity - that's from roughly one gee at your feet to two-thirds of a gee at your head!
That sounds alarming, so lets instead imagine we make the ring/rope 100 m large/long (50 m radius), hence this becomes 1/100 ($10^2$) and is 0.33 $\mathrm{m/s^2}$.
The question is: what is the biological effect of such a gradient in force, as it seems quite likely there is going to be one? How does it compare to the effects of microgravity, especially over the long term? If you have to live with an essentially permanent $0.33\ \mathrm{m/s^2}$ accelerative gradient from your toes to your head for, say, tens of megaseconds (hundreds of days), what would be the effects? (You can assume 1/3 of the time spent sleeping though, if you want) I'm especially thinking of a duration equal to one Mars launch window distance, i.e. the minimum time between an arrival in Mars orbit and departure for the first minimal-energy return to Earth possible. How low would you have to get it to prevent something serious?
Have any tests been done on this? One effect I'm wondering about is altered blood flow throughout the body. Could you get some kind of chronic hypoxia in the brain as a result of the blood being "pushed" toward their feet and away from their head? Would this be compensated by, say, increasing heart rate (and would that lead to severe levels of cardiac stress)? At what levels does it become critical? At what levels does it lead to chronic neuronal death?