Engineers are working on a design for a cylindrical space habitation with a diameter of 4.20 km and length of 32.0 km. The habitation will s

Question

Engineers are working on a design for a cylindrical space habitation with a diameter of 4.20 km and length of 32.0 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 4 times Earth’s gravity?

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Thiên Ân 4 years 2021-08-06T16:08:51+00:00 1 Answers 28 views 0

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  1. MichaelMet
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    2021-08-06T16:10:36+00:00
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    Answer:

    0.14 rad/s

    Explanation:

    We are given that

    Diameter=d=4.2 km

    Radius,r=\frac{d}{2}=\frac{4.2}{2}=2.1 km=2.1\times 1000=2100 m

    Using 1 km=1000  m

    Length,l=32 km

    Acceleration on  its curved walls=g’=4g

    Where g=9.8m/s^2

    We have to find the speed (in rad/s)

    Centripetal acceleration=a_c=\omega^2 r

    \omega^2\times 2100=4\times 9.8

    \omega^2=\frac{4\times 9.8}{2100}

    \omega=\sqrt{\frac{4\times 9.8}{2100}}

    \omega=0.14rad/s

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