Question

One problem for humans living in outer space is that they are apparently weightless. One way around this problem is to design a cylindrical space station that spins about an axis through its center at a constant rate. (See the figure below. (Figure 1)) This spin creates "artificial gravity" at the outside rim of the station.If the diameter of the space station is d = 660 m , how fast must the rim be moving in order for the "artificial gravity" acceleration to be g at the outer rim? (Answer in Rad/s)

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. How fast must the rim move in this case? (Answer in Rad/s)

Answer 1

When the cylinder is rotating with an anguar velocity , Normal reaction between the inner surface of cylinder and astronaut will provide the necessary centripetal acceleration

When we consider the cylinder as a reference frame, it will be a non-inertial frame due to this acceleration. Hence we need to use an inertial force called centrifugal force.

This centrifugal force plays the role of artificial gravity.

Effective acceleration due to gravity

when the artificial acceleration due to gravity is equal to earth's gravity

Angular velocity of cylinder is

when the artificial acceleration due to gravity is equal to earth's gravity

Angular velocity of cylinder is