Artificial Gravity on Luna
It is sometimes stated that while artificial space habitats can be adjusted to any level of centripetal force desired, people living on the Earth's moon or Mars would be stuck with the local ambient gravity. However, it is just as possible to build centrifuges on the moon as to provide the other requirements of good health. Eating and sleeping within a centrifuge sized to accommodate living quarters could provide most of the exercise that people need without requiring much extra time from their schedules. Since much power per person will be required to provide air, food and water, the additional power to keep a centrifuge running is unlikely to make the difference between an economic and a noneconomic settlement.
It's Physically Possible
To provide people with one g acceleration by centrifuge on Luna, there needs to be about 99% of a g radially outward from a vertical axis added to the existing one sixth g. If the centrifuge rotates at a reasonable angular velocity of 2 revolutions per minute, the radius must be 220 meters. To avoid providing a room for the centrifuge with an open space (no pillars) of 440 meters in diameter, the hub of the centrifuge can be left out and the living quarters built in a section of a cylindrical space between 220 meters and 210 meters in radius and between 0 and 15 meters in height. One might imagine that as a circular room of 440 meters in diameter with one big pillar in the middle being 420 meters in diameter. The centrifuge could run constantly except when maintenance requires a shut down. Access to the living quarters could be not by elevator, but by rotavator. People could approach the rotavator on their way home after work, moving through the nonrotating corridors of a lunar base. They could enter the rotavator through a door and start it moving along its circular track just above the centrifuged living quarters. When the rotavator is matched in velocity with the proper portion of the living quarters, people would enter the living quarters through a door. The transition from one sixth g vertical to one g radial could be smoothly accommodated by the floor of the rotavator compartment swinging from downward to radially outward. Experiments on Earth have already shown that most people can exercise in and environment that rotates at 2 rpm without ill effects.
Don't Hold Your Breath
Since this plan calls for a bit more than a one and a third kilometer length of living quarters, it would probably not be built in the first year of operation of a lunar base.
Before many irate readers lambaste this idea for wasting energy consider these power saving features. To reduce air resistance from the floor of the living quarters moving at a speed of 103 miles per hour, the centrifuged living quarters could be built within three nested shells which also rotate. From outer shell to living quarters the speeds of each section would be 25 mph, 51 mph, 77 mph, and 103 mph. The result is that the air resistance loss would be about the same as for a similarly sized doughnut rotating at 26 miles per hour. The drag from the living quarters would pull along the next outer shell and the torque would be passed down to the outermost shell. The savings on air resistance should handily exceed the increased rolling resistance if the shells were carried one on the other by steel wheels or rubber wheels. Shells supported by magnetic levitation should work as well. The rotavator would automatically rendezvous with each shell in turn and transfer to that shell by longitudinal tracks before continuing on circular tracks within each shell. Matched rotavator cars could always operate in synchronization from radially opposite points to reduce asymmetric loading.
As an alternative to nested shells, the room housing the centrifuged living quarters could be pumped down to 0.002 atmospheres pressure and transfers to and from them would go through airlocks. The rotavator would then be a pressurized vehicle. In any case it is not justified to write articles claiming that settlers on Luna would be stuck with one sixth g gravity.
Centrifuged living quarters, as above, could accommodate perhaps 600 people on apartments on two floors with the exact number of residents depending on various matters such as how much space is taken up by providing utilities with liquids being shipped in and out by tank. So why not stay on Earth where 1 g gravity is one of the few things that one can depend upon as being provided with no extra charge? The big draw here is that the industries which will employ people on Luna will ship out their products by some or another kind of electric propulsion and reach customers throughout the solar system at a much smaller cost than shipping products into orbit from Earth. That can not be done as easily from Mars; and setting up such industry on asteroids would be difficult because of the lack of the ability to use remote control devices with a response time of 3 seconds. Luna is the key to the solar system. This is why it is so important to get ground truth from the lunar poles. Hydrogen, carbon, and nitrogen have been observed from frozen volatiles on Luna. If volatiles can be economically extracted, lunar industry is possible. Trade with places where volatiles are cheaper is still in consideration.