Final answer:
To create artificial gravity in a rotating space station, the centripetal acceleration provided by the rotation must mimic the acceleration due to gravity. The equation ω = sqrt(a/r) can be used to calculate the angular velocity required for a desired centripetal acceleration 'a' and radius 'r'. With a diameter of 640m, a rotation period of approximately 36.32 seconds would generate normal gravity in the space station.
Step-by-step explanation:
To create artificial gravity in a rotating space station, the centripetal acceleration provided by the rotation must mimic the acceleration due to gravity. The centripetal acceleration is given by the equation:
a = rω^2
where 'a' is the centripetal acceleration, 'r' is the radius of the space station, and 'ω' is the angular velocity. We can rearrange the equation to solve for angular velocity:
ω = sqrt(a/r)
In this case, we are given that the space station has a diameter of 640m, which means the radius is 320m. Since we want the artificial gravity to be equivalent to normal gravity (9.8m/s²), we can plug in the values and solve for the angular velocity:
ω = sqrt(9.8/320) ≈ 0.173 rad/s
Therefore, a rotation period of approximately 2π/0.173 ≈ 36.32 seconds would create a normal gravity in the space station.