[tex]28[/tex] rotation period will provide "normal" gravity.
According to the question, cylindrical space station 390 meters diameter rotating about its central axis so, the radius of the cylindrical space station is 195 meters.
Now, use the formula [tex]m\omega ^2 r=mg[/tex] where,
[tex]m[/tex] is the mass of the cylindrical space station
[tex]\omega[/tex] is the angular velocity
[tex]r[/tex] is the radius of the cylindrical space station
[tex]g[/tex] is the acceleration due to gravity.
Substitute the parameters and generalise the formula as-
[tex]m\omega ^2 r=mg\\\omega =\sqrt{\dfrac{g}{r}}\\\omega=\sqrt{\dfrac{9.8}{195}}\\\omega=0.22 \;\rm rad/sec[/tex]
Also,
[tex]\omega=\dfrac{2\pi}{T}\\0.22T=2\pi\\T=28.54\;\rm seconds[/tex]
Hence, [tex]28[/tex] rotation period will provide "normal" gravity.
Learn more about angular velocity here:
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