Final answer:
Artificial gravity in a rotating space station can be created using centripetal acceleration. The angular velocity that would produce an artificial gravity of 9.80 m/s² at the rim is approximately 3.13 rad/s.
Step-by-step explanation:
Artificial gravity can be created in a rotating space station by using centripetal acceleration. The astronauts would experience a force that acts towards the center of rotation, simulating the effect of gravity. To calculate the angular velocity that would produce an artificial gravity of 9.80 m/s² at the rim of the station, we can use the formula:
Centripetal acceleration = (angular velocity)² x (radius of rotation).
Given that the diameter of the space station is 200 m, the radius of rotation would be 100 m. Plugging in the values, we have:
(9.80 m/s²) = (angular velocity)² x (100 m).
Solving for the angular velocity, we find that it would be approximately 3.13 rad/s.