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A rotating 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 the 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/s2?Group of answer choices0.313 rad/s0.0980 rad/s10.2 rad/s3.19 rad/s

Question
A rotating 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 the 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/s2?
Group of answer choices
0.313 rad/s
0.0980 rad/s
10.2 rad/s
3.19 rad/s
check_circleAnswer
Step 1

Given:

Diameter of the space station,D = 200 m

Radius, R = 100 m

Artificial gravity(Acceleration) = 9.8 m/s2

Step 2

Calculating the value of angular velocity such that the value of artificial gravity is 9.8 m/s2:

When the station spins, centrifugal force acts...

According to given condition, Centrifugal acceleration should be equal to Artificial gravity
9.8 m/s
Centrifugal acceleration
Centrifugal acceleration= Ra
So, Ro2 =9.8m/s
Substituting values, (100m)a2 = 9.8m/s2
9.8
100
0.313 rad ls
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According to given condition, Centrifugal acceleration should be equal to Artificial gravity 9.8 m/s Centrifugal acceleration Centrifugal acceleration= Ra So, Ro2 =9.8m/s Substituting values, (100m)a2 = 9.8m/s2 9.8 100 0.313 rad ls

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