One way that future space stations may create artificial gravity is by rotating the station.Consider a cylindrical space station 380 m in diameter that is rotating about its longitudinal axis.Astronauts walk on the inside surface of the space station.How long will it take for each rotation of the cylinder if it is to provide "normal" gravity for the astronauts?
A)28 s
B)39 s
C)6.2 s
D)4.4 s

Question

Quizplus · Accepted Answer

To provide "normal" gravity through centripetal acceleration, the space station must simulate Earth's gravity (9.8 m/s^2). The formula for centripetal acceleration is $a = \frac{v^2}{r}$, where $v$ is the tangential velocity and $r$ is the radius of the circle. Since we're dealing with a cylindrical space station, we can also use the formula $a = \omega^2 \times r$, where $\omega$ is the angular velocity in radians per second, and $r$ is the radius of the cylinder. To find the period ($T$), which is the time for one complete rotation, we use the relation $T = \frac{2\pi}{\omega}$.Given that the diameter of the space station is 380 m, the radius ($r$) is half of that, which is 190 m. Setting the centripetal acceleration equal to Earth's gravity gives us:$$9.8 = \omega^2 \times 190$$Solving for $\omega$ gives:$$\omega = \sqrt{\frac{9.8}{190}}$$Then, to find the period ($T$), we use:$$T = \frac{2\pi}{\omega} = \frac{2\pi}{\sqrt{\frac{9.8}{190}}}$$Plugging in the numbers:$$T \approx 28 \text{ seconds}$$Therefore, it will take approximately 28 seconds for each rotation of the cylinder to provide "normal" gravity for the astronauts.

One Way That Future Space Stations May Create Artificial Gravity