Final answer:
The angular velocity that would produce an artificial gravity of 9.80 m/s² at the rim of the space station is approximately 0.465 rad/s.
Step-by-step explanation:
To find the angular velocity that would produce an artificial gravity of 9.80 m/s² at the rim of the space station, we can use the formula for centripetal acceleration:
ac = w²r
Where:
- ac is the centripetal acceleration
- w is the angular velocity
- r is the radius
We can rearrange the formula to solve for angular velocity:
w = sqrt(ac / r)
Substituting ac = 9.80 m/s² and r = 95 m (half the diameter) into the formula, we get:
w = sqrt(9.80 m/s² / 95 m) = 0.465 rad/s
Therefore, the angular velocity that would produce an artificial gravity of 9.80 m/s² at the rim of the space station is approximately 0.465 rad/s.