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Engineers are working on a design for a cylindrical space habitation with a diameter of 7.50 km and length of 29.0 km. The habitation will simulate gravity by rotating along its axis. With what speed (in rad/s) should the habitation rotate so that the acceleration on its inner curved walls equals 8 times Earth's gravity

Respuesta :

Cricetus

Answer:

The speed will be "0.144 rad/s".

Explanation:

Given that,

Diameter,

d = 7.50 km

Radius,

R = [tex]\frac{7.5}{2} \ Km[/tex]

Acceleration on inner curve,

= 8 times

Now,

As we know,

⇒ [tex]\omega^2R=8g[/tex]

or,

⇒ [tex]\omega=\sqrt{\frac{8g}{R} }[/tex]

On substituting the values, we get

⇒     [tex]=\sqrt{\frac{8\times 9.8}{\frac{7.5}{2}\times 10^3 } }[/tex]

⇒     [tex]=\sqrt{\frac{78.4}{3750} }[/tex]

⇒     [tex]=\sqrt{0.0209}[/tex]

⇒     [tex]=0.144 \ rad/s[/tex]

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