Question

You want to create a space station that is 50 meters in radius. If you want it to simulate Earth's gravitation, how fast must it go?

Answer 1

w = 0.196 rad / s

Step-by-step explanation:

To generate an acceleration similar to that of the earth, the station's centripetal acceleration must be equal to the acceleration due to gravity.

a_c = v² / r = w² r

a_c = g

we substitute

g = w² r

w² = g / r

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

let's calculate

w = √9.8/50

w = 0.196 rad / s

therefore the station must rotate at that angular velocity so that the acceleration in the outer wall is equal to the ratio of gravity