Future space stations will create an artificial gravity by rotating. Consider a cylindrical space station 100 m diameter rotating about its

Question

Future space stations will create an artificial gravity by rotating. Consider a cylindrical space station 100 m diameter rotating about its central axis. Astronauts walk on the inside surface of the space station. What rotation period will provide “normal” gravity?

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Bơ 4 years 2021-08-06T21:22:16+00:00 1 Answers 65 views 0

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  1. thongdat2
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    2021-08-06T21:23:16+00:00
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    Given Information:

    Diameter = d = 100 m

    Required Information:

    Period = T = ?

    Answer:

    Period = T = 14.2 seconds

    Explanation:

    We know that a station revolving  at an angular velocity ω,  have an  acceleration given by

    α = ω²r

    Where ω is angular velocity and r is the radius of cylindrical space station.

    Normal gravity means α = g = 9.8 m/s²

    ω² = α/r

    ω = √(α/r)

    The radius is given by

    r = d/2

    r = 100/2

    r = 50 m

    ω = √(9.8/50)

    ω = 0.4427 rad/sec

    We also know that

    ω = 2πf

    f = ω/2π

    f = 0.4427/2π

    f = 0.0704 rev/sec

    Finally time period is given by

    T = 1/f

    T = 1/0.0704

    T = 14.2  sec

    Therefore, the rotation period is 14.2 seconds.

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