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12 July, 02:14

A space station, in the form of a wheel 119 m in diameter, rotates to provide an "artificial gravity" of 2.20 m/s2 for persons who walk around on the inner wall of the outer rim. find the rate of the wheel's rotation in revolutions per minute that will produce this effect.

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  1. 12 July, 02:19
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    Well, since it's in the shape of a wheel and the person walks around the edge of it, they must have a centripetal acceleration. Since a=v^2/r you can solve for "v" using 2.20 as your "a" and 59.5 as your "r" (r=half of the diameter).

    a=v^2/r

    v = (a*r) ^ (1/2) = ((2.20) * (59.5)) ^ (1/2) = 11.44 m/s.

    After you get "v," plugged that into T=2 pi r / v. This will give you the 1rev per sec.

    T=2 pi r / v = T = (2) * (pi) * (59.5) / (11.44) = 32.68 rev/s

    Use dimensional analysis to get rev per min (1rev / # sec) times (60 sec/min).

    (32.68 rev/s) (60 s/min) = 1960.74 rev/min
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