   Chapter 7, Problem 16P

Chapter
Section
Textbook Problem

It has been suggested that rotating cylinders about 10 mi long and 5.0 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?

To determine
The angular speed of the cylinder so that the centripetal acceleration at the surface will be equal to the free fall acceleration.

Explanation

Given info: The length of the cylinder is 10mi . The diameter of the cylinder is 5.0mi .

Explanation:

The centripetal acceleration of the cylinder is given by,

ac=rω2

• r is the radius of the cylinder
• ω is the angular speed of the cylinder

The angular speed of the cylinder will be,

ω=acr

In terms of the diameter of the cylinder, the angular speed will be,

ω=2acd

Substitute 9.80ms-2 for ac , 5.0mi for d to determine the angular speed of the cylinder,

ω=2(9

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