Question

What period of rotation would be required in a 1.0km diameter circular space station in order to achieve a centripetal acceleration equivalent to the acceleration due to gravity at Earth's surface?

Answer 1

For circular motion, the centripetal acceleration is given by,

--------(1)

where are respectively the tangential velocity and radius. The time that is needed for one complete revolution is called the time period and denoted by .

When velocity is constant, we have,

--------(2)

Using Eq (2) in Eq (1), we get,

Given, radius, (diameter)/2 = (1.0 km)/2 = 500 m. Also,

(= acceleration due to gravity at Earth's surface) = 9.8 m/s² . Plugging in the values, we get,

44.88 s.