The space station must have an angular speed of 1733.5 rev/day
Explanation:
The centripetal acceleration felt by an object in circular motion is given by:
[tex]a = \omega^2 r[/tex]
where
[tex]\omega[/tex] is the angular speed
r is the radius of the circle
In this problem, we want the acceleration to be:
[tex]a=0.9 g = (0.9)(9.8 m/s^2)=8.8 m/s^2[/tex]
The diameter of the circle is 1.1 km, so the radius is
[tex]r=\frac{1.1 km}{2}=550 m[/tex]
So we can use the equation above to find the angular speed that the space station must have:
[tex]\omega=\sqrt{\frac{a}{r}}=\sqrt{\frac{8.8}{550}}=0.126 rad/s[/tex]
Now we have to convert into revolutions per day. We have:
[tex]1 rev = 2\pi rad[/tex]
[tex]1 day = 86400 s[/tex]
Therefore,
[tex]\omega = 0.126 \frac{rad}{s} \cdot \frac{86400 s/d}{2\pi rad/rev}=1733.5 rev/day[/tex]
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