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

Question #246138

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


1
Expert's answer
2021-10-05T15:44:25-0400

Solution.

a=9.8m/s2;a=9.8 m/s^2;

d=3.94mi=6340.815m;d=3.94 mi=6340.815m;

a=v2r    v2=ar;a=\dfrac{v^2}{r}\implies v^2=ar;

v2=9.8m/s23170.4=31070(m/s)2;v^2=9.8m/s^2\sdot3170.4=31070(m/s)^2;

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

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

Answer: 0.056 rad/s.


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