Question

Engineers are working on a design for a cylindrical space habitation with a diameter of 7.50 km and length of 29.0 km. The habitation will simulate gravity by rotating along its axis. With what speed (in rad/s) should the habitation rotate so that the acceleration on its inner curved walls equals 8 times Earth's gravity

Answer 1

The speed will be "0.144 rad/s".

Step-by-step explanation:

Given that,

Diameter,

d = 7.50 km

Radius,

R =
`(7.5)/(2) \ Km`

Acceleration on inner curve,

= 8 times

Now,

As we know,

⇒
`\omega^2R=8g`

or,

⇒
`\omega=\sqrt{(8g)/(R) }`

On substituting the values, we get

⇒
`=\sqrt{(8* 9.8)/((7.5)/(2)* 10^3 ) }`

⇒
`=\sqrt{(78.4)/(3750) }`

⇒
`=√(0.0209)`

⇒
`=0.144 \ rad/s`