Question

It has been suggested that rotating cylinders about 19.5 mi long and 5.66 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

_____rad/s

Answer 1

The angular speed such a cylinder must have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth is 0.046 rad/s.

Angular speed of the cylinder

The angular speed such a cylinder must have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth is calculated as follows;

a = v²/r

v² = ar

(ωr)² = ar

ω²r² = ar

ω²r = a

ω² = a/r

ω = √(a/r)

where;

• a is centripetal acceleration = acceleration due to gravity, g
• r is radius of the cylinder = 5.66 m / 2 = 2.83 mi = 4554.4 m
• ω is angular speed

ω = √(g/r)

ω =  √(9.8/4554.4)

ω = 0.046 rad/s

Thus, the angular speed such a cylinder must have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth is 0.046 rad/s.

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