Calculating the Angular Speed of a Rotating Space Station Ring

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To achieve a sensation of 0.411 g for occupants in a rotating space station ring with a diameter of 50.3 m, the required centripetal acceleration must be calculated as 0.411 times 9.8 m/s², resulting in approximately 4.02 m/s². Using the formula Ac = V²/r, where r is the radius of the ring (25.15 m), the necessary velocity can be derived. By rearranging the equation, the velocity needed to create this acceleration is found to be about 11.25 m/s. Subsequently, the angular speed can be calculated using the relationship between linear velocity and angular speed. This analysis provides the necessary parameters for designing a rotating space station that simulates gravity.
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A proposed space station includes living quarters in a circular ring 50.3 m in diameter. At what angular speed should the ring rotate so the occupants feel 0.411 g where g is the gravitational acceleration on the surface of the Earth?
 
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Ac= (V^2/r); where Ac is the centripetal acceleration (aka gravity) V is the velocity at which the object is rotating and r is the radius.


One g is 9.8 m/s^2

Find the numerical value for 0.411 g's; plug this into the equation and you can find the velocity necessary to obtain 0.411 g's.
 

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