Question

A proposed space station includes living quarters in a circular ring 45.0 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

Angular speed,
`\omega=0.65\ rad/s`

Step-by-step explanation:

Given that,

Diameter of the circular ring, D = 45 m

Radius, r = 22.5 m

Let
`\omega` is the angular speed should the ring rotate so the occupants feel that they have the same weight as they do on Earth. It can be given by providing the centripetal force to the normal force as :

`mg=m\omega^2r`

`\omega=\sqrt{(g)/(r)}`

`\omega=\sqrt{(9.8\ m/s^2)/(22.5\ m)}`

`\omega=0.65\ rad/s`

So, the angular speed of the ring is 0.65 rad/s. Hence, this is the required solution.