Question

Engineers are working on a design for a cylindrical space habitation with a diameter of 8 km. and length of 50. 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 4 times Earth's gravity?____rad /s

Answer 1

Answer:

ω = 0.098 rad/s

Explanation:

given,

diameter = 8 Km

length = 50 Km

the acceleration on its inner curved walls equals 4 times Earth's gravity

now,

equating centripetal acceleration = 4 x Earth's gravity

ω² r = 4 g

$\omega = \sqrt{\dfrac{4g}{r}}$

$\omega = \sqrt{\dfrac{4\times 9.8}{4000}}$

$\omega = \sqrt{0.0098}$

 ω = 0.098 rad/s

the angular speed at which habitation rotate is equal to 0.098 rad/s