A cylindrical space colony 8.00 km in diameter and 30.0 km long has been proposed as living quarters for future space explorers.Such a habitat would have cities,land,and lakes on the inside surface and air and clouds in the center.All this would be held in place by the rotation of the cylinder about the long axis.How fast would such a cylinder have to rotate to produce a 1-g gravitational field at the walls of the cylinder?

Question

Quizplus · Accepted Answer

The gravitational acceleration at the walls of the cylinder is given by:

g = ω²r

where ω is the angular velocity, and r is the radius of the cylinder.

We want g to be equal to 9.81 m/s² (1 g), and r = 4.00 km (half the diameter of the cylinder).

So, we have:

9.81 m/s² = ω²(4.00 km)

We need to convert km to meters, and solve for ω:

ω = √(9.81 m/s² / 4.00 km) = 0.049 rad/s

Therefore, the cylinder would need to rotate at 0.049 rad/s to produce a 1-g gravitational field at the walls of the cylinder.

The best choice is A).

A Cylindrical Space Colony 8