Rotating Space Stations.? One problem for humans living in outer space is that they are apparently weightless. One way around this problem is to design a space station that spins about its center at a constant rate. This creates “artificial gravity” at the outside rim of the station. (a) If the diameter of the space station is 800 m, how many revolutions per minute are needed for the “artificial gravity” acceleration to be 9.80 m/s2? (b) If the space station is a waiting area for travelers going to Mars, it might be desirable to simulate the acceleration due to gravity on the Martian surface (3.70 m/s2). How many revolutions per minute are needed in this case?

Solution 49E The diameter of the space station is 800 m. So, the radius will be 800/2 = 400 m. As it is rotating about it’s centre, the centripetal acceleration felt by a person sitting at the circumference will be, a = v / r---------------------(1) The radius we already know, so let’s put the value in equation (1) to get the angular velocity. But angular velocity is defined by the relation, = 2/T --------------------(2) Where T is the time period of revolution. And the velocity is defined as, v = 2r/ T --------------------(3) So, the angular velocity and the velocity are related as, = v/r----------------(4) v = r------------------(5) If we put this result in equation...