Question

A proposed space station includes living quarters in a circular ring 64.0 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

`w=0.5534rad/s`

Step-by-step explanation:

Given data

Diameter d=64.0 m

To find

Angular velocity ω

Solution

From Centripetal acceleration we know that

`a=g=(v^(2) )/(R)`

As we know that angular velocity ω as

`w=v/R\\v=wR`

So

`g=(v^(2) )/(R)\\g=((wR)^(2) )/(R)\\ g=(w^(2)R^(2) )/(R)\\g=w^(2)R\\w^(2)=(g)/(diameter/2)\\w^(2)=(9.8m/s^(2))/((64/2)m)\\w^(2)=0.30625\\w=√(0.30625)\\ w=0.5534rad/s`