In the movie The Martian, astronauts travel to Mars in a spaceship called Hermes. This ship has a ring module that rotates around the ship to create "artificial gravity" within the module. Astronauts standing inside the ring module on the outer rim feel like they are standing on the surface of the Earth. (The trailer for this movie shows Hermes at t=2:19 and demonstrates the "artificial gravity" concept between t= 2:19 and t=2:24.)Analyzing a still frame from the trailer and using the height of the actress to set the scale, you determine that the distance from the center of the ship to the outer rim of the ring module is 11.60 ma)What does the rotational speed of the ring module have to be so that an astronaut standing on the outer rim of the ring module feels like they are standing on the surface of the Earth?

The equation that relates rotational speed with centripetal acceleration is [tex]a_{cp}=\omega^2r[/tex]. For our case we want to know how much has to be the rotational speed of the ring module of radius [tex]r=11.6m[/tex] in order to achieve a centripetal acceleration equal to [tex]g=9.8m/s^2[/tex], which will be the acceleration felt by the astronauts.

We write then our equation as:

[tex]\omega=\sqrt{\frac{a_{cp}}{r}}[/tex]

Which for our values is:

[tex]\omega=\sqrt{\frac{a_{cp}}{r}}=\sqrt{\frac{9.8m/s^2}{11.6m}}=0.92rad/s[/tex]