Answer to Question #246138 in Molecular Physics | Thermodynamics for Kelani

Question

It has been suggested that rotating cylinders about 14.0 mi long and 3.94 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

___rad/s

Answer 1

Solution.

$a=9.8 m/s^2;$

$d=3.94 mi=6340.815m;$

$a=\dfrac{v^2}{r}\implies v^2=ar;$

$v^2=9.8m/s^2\sdot3170.4=31070(m/s)^2;$

$v=\sqrt{31070}=176.27m/s;$

$w=\dfrac{v}{r}=0.056 rad/s;$

Answer: 0.056 rad/s.