Answer:
0.05 rad/s
Explanation:
7.8 km = 7800 m
For the residents inside the space cylinder to experience the same gravitation acceleration g = 9.81m/s2 on Earth, the centripetal acceleration must be the same as g
[tex]a = g[/tex]
But centripetal acceleration is product of angular velocity squared and radius of rotation r
[tex]\omega^2r = 9.81[/tex]
[tex]\omega^2 d/2 = 9.81 [/tex]
[tex]\omega^2 = \frac{2*9.81}{d} = \frac{19.62}{7800} = 0.0025[/tex]
[tex]\omega = \sqrt{0.0025} = 0.05 rad/s[/tex]
The angular speed of the cylinder is 0.050 rad/s.
The angular velocity is defined as the velocity at which an object revolves about an axis within a given time interval.
Given that the length l of the cylinder is 16 km and the diameter is 7.8 km. Also given that the residents on it will experience the same acceleration due to gravity as on Earth, hence the centripetal acceleration will be equivalent to g = 9.8 m/s2.
The angular velocity can be calculated by the centripetal acceleration of the cylinder.
[tex]a = \omega ^2r[/tex]
Where a is centripetal acceleration, [tex]\omega[/tex] is angular velocity and r is the radius of the cylinder.
[tex]g = \omega ^2 \times \dfrac {d}{2}[/tex]
Where g is the gravitational acceleration and d is the diameter of the cylinder. Substituting the values in the above formula, we get the angular velocity.
[tex]9.8 = \omega ^2 \times \dfrac {7800}{2}[/tex]
[tex]\omega = \sqrt {\dfrac {9.8\times 2}{7800}}[/tex]
[tex]\omega = 0.050 \;\rm rad/s[/tex]
Hence we can conclude that the angular speed of the cylinder is 0.050 rad/s.
To know more about the angular velocity, follow the link given below.
https://brainly.com/question/1980605.
