Rotating Spacecraft

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Unit: Uniform Circular Motion and Gravitation

Prerequisites

Equivalence Principle

Later Topics

None

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Part 1

A rotating cylindrical spacecraft is designed to produce artificial gravity through centripetal acceleration. At the outer radius $R_{\text{outer}} = \text{30.4}\,\text{m}$ , the artificial gravity must be $g_{\text{outer}} = \text{9.8}\,\text{m/s}^2$ . Calculate the angular velocity $\omega$ (in rad/s) of the spacecraft required to produce this artificial gravity at the outer radius.

Correct!

Solution:

Solution

The artificial gravity is produced by centripetal acceleration. At radius $R_{\text{outer}}$ , a person experiences centripetal acceleration:

a_c = \omega^2 R_{\text{outer}}

Setting this equal to the desired artificial gravity $g_{\text{outer}}$ :

\omega^2 R_{\text{outer}} = g_{\text{outer}}

Solving for $\omega$ :

\omega = \sqrt{\frac{g_{\text{outer}}}{R_{\text{outer}}}}

Substituting the given values:

\omega = \sqrt{\frac{\text{9.8}}{\text{30.4}}} = \text{0.57}\,\text{rad/s}

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