So I’m building a moon base and I want some 1G working environments for exercise and … whatnot. So I build a giant turntable to spin some rooms. What angle do they need to be at to get 1G vertical to their floors, and how fast do I need to spin the rig?
Easy questions, but I’m feeling lazy and I’m busy trying to figure out how to produce all necessary resources locally on the moon. 
Deleted. Changed my mind. This sounds like homework.
Been too long since physics 101 for me to answer the question asked. I’d just like to point out the inherent problems with spinning a slope floor gym up to the point where you’d have an effective 1G environment.
Entrance and egress. Getting in and out would be an issue. The most elegant solution would be that the gym was actually bowl shaped and users would get in and out via some sort of catwalk to the center. Then walk out to the workout area at perimeter under a gradually increasing centrifugal (centripital?) load.
Then you have the whole issue of dynamically balancing it.
I’m thinking a better solution would be some varient of a weight suit. Inertia would be off, but that would really only affect people who were doing combat sparring.
Just hang the rooms such that they can lift up as they spin. They will automatically angle themselves to the angle that will make all the force feel “down”. As for the speed, that will depend on the diameter of your ‘turntable’.
Hollow out the moon and spin it a lot faster. You’ll be able to walk around the inner surface of the moon at it’s equator. I’m not sure but there may some logistical problems with this approach.
You have to spin them almost as fast as if you wanted 1G horizontally. The Moon’s gravity is about 1/6th of Earth’s, so you’d need sqrt(1-1/6^2) = 0.986 G horizontally. Get your angle from a right triangle with one side = 1/6 and the hypotenuse = 1. (ETA: 9.6 degrees, almost vertical.)
Yeah, I did the math when the only reply was standingwave thinking I needed homework assistance. I actually teach physics, and was just lazy.
And almost vertical is no good for large structures, but I could always have some small exercise carousels.
The smaller the confines, the faster it needs to spin.
If you make something like a hamster ball, the differential spin would be too great to be useful.
But a huge carousel might be ridiculous.
Personally, I like the rotating dish concept.
How many people need to be under 1-G?
Inflate a dome and put a basketball court in it.The colonists will get plenty of exercise, and we get spectacular jump shots.
They won’t get as much as they would from basketball on Earth since they’d be spending much more time in the air.
Imagine playing any sport that involves throwing balls (or any kinds of projectiles) in that environment! You’d have to learn to compensate for coriolis force. The ball’s path would look very strange to those of us who didn’t grow up using such exercise venues.