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6 May, 22:42

It has been suggested that rotating cylinders about 10 mi long and 5.0 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

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  1. 7 May, 02:09
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    Centripetal acceleration is given by:

    a = v²/r

    a = centripetal acceleration, v = speed of cylinder at surface, r = radius of cylinder

    This equation relates the speed of the cylinder at its surface to its angular velocity:

    v = rω

    v = speed at surface, r = radius, ω = angular velocity

    Make a substitution:

    a = (rω) ²/r

    a = rω²

    Given values:

    a = 9.81m/s², r = (5.0mi) / 2 = 2.5mi = 4023m

    Plug in and solve for ω:

    9.81 = 4023ω²

    ω = 0.049rad/s
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