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The Empire's space station is a long way from any star. It is circular and has a radius of 5. 10 km. The angular velocity that is needed to give the station an artificial gravity of 9. 80 ms2/ at its circumference is:___.


A) 4. 4 times 10^-2 rad/s.


B) 7. 0 times 10^-3 rad/s.


C) 0. 28 rad/s.


D) -0. 22 rad/s.


E) 1. 3 times 10^3 rad/s

Respuesta :

Answer:

A

Explanation:

r= 5100m

acceleration of center=g= [tex]\frac{v^{2} }{r}[/tex]

v= rw, Which is angular velocity X radius

put this in acceleration of center equation

= [tex]\frac{(rw)^{2} }{r} =g[/tex]

= [tex]rw^{2} =g[/tex]

= [tex]5100 . w^{2} = 9.8[/tex]

[tex]w^{2} = 0.0019[/tex]

=[tex]\sqrt{0.0019} = 0.0438[/tex]

which is approximately A.

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