Question

A cylindrical space colony 8km in diameter and 30 km long hasbeen proposed as living quarters for future space explorers. Such a habitat would have cities, land and lakes on the insidesurface and air and clouds in the center. All this would beheld in place by the rotation of the cylinder about the longaxis. How fast would such a cylinder have to rotate toproduce a 1-g gravitational field at the walls of thecylinder?
a) 0.05 rad/s
b) 0.10 rad/s
c) 0.15 rad/s
d) 0.20 rad/s
e) 0.25 rad./s

Answer 1

Answer:

A.

Explanation:

To solve this problem it is necessary to take into account the concepts related to angular velocity and centripetal acceleration,

from the cinematic equations of motion we know that

$V= r\omega$

where,

V = Tangential Velocity

r = radius

$\omega =$ Angular velocity

While the centripetal acceleration is given by

$a = r \omega^2$

The displacement of the object is based on gravitational acceleration, so

a = g = 9.8 and the radius would be

$r = \frac{d}{2} = \frac{8}{2} = 4000m$

Reemplazando:

$\omega^2=\frac{g}{R}$

$\omega= \sqrt{\frac{g}{R}}$

$\omega = \sqrt{\frac{9.8}{4000}}$

$\omega = 0.04949rad/s \approx 0.5rad/s$

Therefore the answer is A.