Question

future space stations will create an artifical gravity by rotating. consider a cylinderical space station 640m diameter rotating about its central axis. astronauts walk on the inside surface of thje space station. what rotation period will be normal gravity

Answer 1

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.