# physics

posted by anon

A cylindrical space colony 8 km in radius and 60 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?

1. MathMate

Being a space station, there will be no (appreciable) gravity due to the mass of the space station. By rotating the cylinder about the long axis, the walls of the cylinder will be subject to a centrifugal acceleration that is proportional to the square of the rotational velocity of the cylinder.

Centrifugal acceleration, g
= rω²

r = 8km = 8000 m
g = 9.81 m s-2

9.81 = 8000 ω²
ω² = 9.81/8000
ω = sqrt(9.81/8000)

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