Question

A rotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. If the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of 9.80 m/s^{2} 2 at the rim?

Answer 1

Answer: 0.313 rad/s

Explanation:

The equation that relates the velocity $V$ and the angular velocity $\omega$ in the uniform circular motion is:

$V=\omega.r$   (1)

Where $r=d/2=100m$ is the radius of the space station (with a diaeter of 200m) that describes the uniform circular motion.

Isolating $\omega$ from (1):

$\omega=\frac{V}{r}$  (2)

On the other hand, we are told the “artificial gravity” produced by the cetripetal acceleration $a_{c}$ is $9.8m/s^{2}$, and is given by the following equation:

$a_{c}=\frac{V^{2}}{r}$   (3)

Isolating $V$:

$V=\sqrt{a_{c}.r}$   (4)

$V=31.3049m/s$   (5)

Substitutinng (5) in (2):

$\omega=\frac{31.3049m/s}{100m}$  (6)

$\omega=0.313rad/s$ This is the angular velocity that would produce an “artificial gravity” of 9 $9.8m/s^{2}$.