Question

A proposed space station includes living quarters in a circular ring 58.0 m in diameter. At what angular speed should the ring rotate so the occupants feel that they have the same weight as they do on Earth

Answer 1

The angular speed
`w = 0.5813 \ rad/s`

Step-by-step explanation:

From the question we are told that

The diameter is d = 58.0 m

Generally for the occupants feel that they have the same weight as they do on Earth then the centripetal acceleration of the circular ring must be equal to the acceleration due to gravity this can be mathematically represented as

`a_c = g`

Here
`a_c` is the centripetal acceleration which is mathematically represented as

`a_c = w^2 * r`

Here r is the radius of the circular ring

=>
`w^2 * r = g`

=>
`w = \sqrt{(g)/(r) }`

=>
`w = \sqrt{(9.8)/( (d)/(2) ) }`

=>
`w = \sqrt{(9.8)/( (58.0 )/(2) ) }`

=>
`w = 0.5813 \ rad/s`