Any mathematicians or physicists out there? I'm working on a story that takes place on a torus-shaped space station. Assuming the torus is one mile in radius (1584 meters) and revolving around its center, I'm trying to calculate what the rotational period of the station would have to be in order for a person standing inside the rim to feel centripetal acceleration equivalent to 1 gee—9.8 m/s2, that is.
It's been a long time since college physics for me, but my calculations using the formula
ac = ω2rwhere ac is centripetal acceleration, r is the radius and the angular velocity ω is
| ω = | Δθ |
| Δt |
and solving for time Δt when the arc Δθ is 2π radians, seems to show that the rotational period would have to be about 79.88 seconds, or one rotation every one minute and twenty seconds. (Basically, I plugged the lower formula into the upper one and solved for Δt.)
Can anyone verify this result?
