It has been suggested that rotating cylinders about 11 mi long and 4.1 mi in dia

Question

It has been suggested that rotating cylinders about 11 mi long and 4.1 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?

Explanation / Answer

we want to equate centrip force due to rotation with the gravity felt on the surface of the earth, or mv^2/r=mg => v^2=rg in this case, we envision rotation about the long axis of the ship, so that r, the distance from the rotation axis, is the radius of the cylinder and is 42mi/2=2.1mi convert to MKS: 2.1mile=3380m g=9.8m/s/s v=sqrt[r g]=182m/s the time it would take to make one revolution would be 2 pi r/speed = 6.3s

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