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Engineers and science fiction writers have proposed designing space stations in the shape of a rotating wheel or ring, which would allow astronauts to experience a sort of artificial gravity when walking along the inner wall of the station's outer rim. (a) Imagine one such station with a diameter of 121 m, where the apparent gravity is 2.60 m/s2 at the outer rim. How fast is the station rotating in revolutions per minute?

Respuesta :

Answer:

w = 1.976 rpm

Explanation:

For simulate the gravity we will use the centripetal aceleration [tex]a_c[/tex], so:

[tex]a_c = w^2r[/tex]

where w is the angular aceleration and r the radius.

We know by the question that:

r = 60.5m

[tex]a_c[/tex] = 2.6m/s2

So, Replacing the data, and solving for w, we get:

[tex]2.6m/s = w^2(60.5m)[/tex]

W = 0.207 rad/s

Finally we change the angular velocity from rad/s to rpm as:

W = 0.207 rad/s = 0.207*60/(2[tex]\pi[/tex])= 1.976 rpm

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