Question

What should be the radius of a space station spinning with an angular speed of 2 rpm such that an astronaut inside the station experiences artificial gravity with g = 10 m /s2

Answer 1

Answer on Question #66050, Physics / Mechanics | Relativity

Question:

What should be the radius of a space station spinning with an angular speed of 2 rpm such that an astronaut inside the station experiences artificial gravity with $g = 10 \, \text{m/s}^2$?

Solution:

In this case artificial gravity occurs due to centrifugal force.

Therefore centrifugal acceleration $a_{cf} = \omega^2 R = g$, where $\omega$ — angular velocity and $R$ — the radius of the space station.

$$\omega^2 R = g \Rightarrow R = \frac{g}{\omega^2}.$$ $$\omega = 2 \, r p m = 2 \cdot \frac{2\pi}{60} s^{-1} = \frac{\pi}{15} s^{-1}$$ $$R = \frac{g}{\omega^2} = \frac{10}{\left(\frac{\pi}{15}\right)^2} = \frac{2250}{\pi^2} \cong 228 \, m$$

Answer:

$$228 \, m$$

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