Arotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. the outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. if the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of 9.80 m/s^{2} 2 at the rim?

Centripetal acceleration is towards the center. The angular velocity of the rim that will produce the artificial gravity is 9.80 m/s².

The centripetal acceleration is caused due to change in direction of the body which is in a circular motion, the acceleration is towards the center of the circle. It is calculated using the formula,

We know that the acceleration produced by centripetal acceleration can be given as,

,

We also know that the velocity in the form of angular velocity can be written as,

Substituting the value of the velocity in the acceleration, we will get,

As it is given to us that the acceleration of the artificial gravity is 9.80 m/s², while the radius is 200 m, and we know that the radius is half the diameter, therefore, the angular velocity can be written as,

Hence, the angular velocity of the rim that will produce the artificial gravity is 9.80 m/s².

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0.313 rad/s

Explanation:

The equation that relates the velocity and the angular velocity in the uniform circular motion is:

  (1)

Where is the radius of the space station (with a diaeter of 200m) that describes the uniform circular motion.

Isolating from (1):

 (2)

On the other hand, we are told the “artificial gravity” produced by the cetripetal acceleration is , and is given by the following equation:

  (3)

Isolating :

  (4)

  (5)

Substitutinng (5) in (2):

 (6)

This is the angular velocity that would produce an “artificial gravity” of 9 .

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