Exploring the Effects of Rotation on Astronauts in a Spinning Space Station

[ahrog]

Homework Statement

One design for orbitting space stations has a structure that is very much like a large wheel. The astronauts live near the rim, where the spinning of the wheel provides an acceleration that mimics the effects of gravity.
a) If the station has a diameter of 94m, what period of rotation would be required for the astronauts at the rim to experience an acceleration similar to the acceleration of gravity on earth?
b) Imagine that you are sitting motionless in a spacecraft outside the space station. You are watching the space station spin. Explain the effects on the astronauts who are spinning in the space station from your frame of reference.
c) Imagine that you are now an astronaut on the space station. Explain the effects on your body from this frame of reference.

Homework Equations

Ac= v²/r
v= 2pir/t
Fc=mv²/r
Gravity on Earth = 9.8 m/s²

The Attempt at a Solution

a) Yet again my textbook and module booklet give me absolutely no help towards this problem. I know I need to find the revolutions per second or how long it takes for a revolution to occur. I don't know how to get this number though. The only way I can think of is guess and check...lol Please help!
b) I'm guessing they want something along the lines of the person outside is seeing the astronaauts maintain a velocity as they rotate around the space station. However, they give a very large answer box, and I'm not sure how I should expand on this idea...
c) I'm guessing the person is not feeling much of a difference in the space station as they would on earth, as the rotation is keeping artificial gravity. The person has a centrifugal force pinning him down to the side.

 

[tiny-tim]

a) If the station has a diameter of 94m, what period of rotation would be required for the astronauts at the rim to experience an acceleration similar to the acceleration of gravity on earth?
…
Ac= v²/r
v= 2pir/t
Fc=mv²/r
Gravity on Earth = 9.8 m/s²
…
a) I know I need to find the revolutions per second or how long it takes for a revolution to occur. I don't know how to get this number though.

Hi ahrog!

(have an omega: ω )

You have all the equations there …

just use v = rω.

 

[thomate1]

However, when he looks out the window, he can see the person outside the space station moving at a constant velocity. Again, I'm not sure how to expand on this idea as the answer box is quite large.

I would like to address the content by first acknowledging the potential benefits of using a spinning space station design to provide artificial gravity for astronauts. This could potentially reduce the negative effects of long-term weightlessness on the human body.

a) To calculate the period of rotation required for the astronauts at the rim to experience an acceleration similar to the acceleration of gravity on Earth, we can use the equation Ac = v^2/r, where Ac is the centripetal acceleration, v is the tangential velocity, and r is the radius of the space station. We can also use the equation v = 2πr/t, where t is the period of rotation. By setting these two equations equal to each other and solving for t, we can find the period of rotation required. In this case, the radius is given as 94m and the acceleration of gravity on Earth is 9.8 m/s^2. Plugging in these values, we get a period of rotation of approximately 62 seconds.

b) From the perspective of someone outside the space station, the astronauts inside would appear to be moving at a constant velocity as they rotate around the station. This is due to their tangential velocity, which remains constant as they move in a circular motion. However, from this frame of reference, the astronauts may also appear to be experiencing a centripetal force, which is the force that keeps them moving in a circular path. This force would be directed towards the center of rotation and would be responsible for the artificial gravity experienced by the astronauts.

c) As an astronaut on the space station, the effects on your body would depend on your distance from the center of rotation. If you are at the rim, you would experience a centrifugal force pushing you towards the outer edge of the station, which would mimic the effects of gravity. However, if you were closer to the center of rotation, this force would be lessened. Additionally, you may also experience some dizziness or disorientation due to the constant rotation. From your perspective, the person outside the space station may appear to be moving at a constant velocity, but you would also feel a force pushing you towards the outer edge of the station, which may appear to be an artificial