Future space stations will create an artificial gravity by rotating.Consider a cylindrical space station 390 m diameter rotating about its central axis.Astronauts walk on the inside surface of the space station.What rotation period will provide "normal" gravity?
A) 28 s
B) 40 s
C) 6.3 s
D) 4.4 s

Question

Quizplus · Accepted Answer

To provide "normal" gravity, the centripetal acceleration at the surface must equal the acceleration due to gravity on Earth ($g = 9.8 \, \text{m/s}^2$). The formula for centripetal acceleration is $a = \frac{v^2}{r}$, where $v$ is the linear velocity and $r$ is the radius of the circle. Since $v = \frac{2\pi r}{T}$, where $T$ is the period, we can substitute $v$ into the acceleration formula to get $a = \frac{4\pi^2 r}{T^2}$. Setting $a = g$ and solving for $T$ gives $T = \sqrt{\frac{4\pi^2 r}{g}}$. The radius $r$ is half the diameter, so $r = 195 \, \text{m}$. Plugging in the values gives $T = \sqrt{\frac{4\pi^2 \times 195}{9.8}} \approx 28 \, \text{s}$.

Future Space Stations Will Create an Artificial Gravity by Rotating