Rotation of cylindrical habitat in space

[tubworld]

I have this question on this article by G.K. O'Neill,1974. who proposed having a cylindrical habitat in space. Then the article posed a question asking me to ponder on the speed of the rotation of the cylinder such that it wld imitate Earth's gravitational field at the walls of the cylinder given that it is 6.07 km in diameter and 30km long. It rotates abt its long axis. My working is as follows but am unsure if I am right cos I don't seem to use the information on the length of the cylinder.

radius = 6.07/2km
Since rw^2 = 9.8, and w = 2PI * f, where w=angular velocity and f=frequency,

we solve for f to get the ans.

From what I have the ans for f is 0.009043859 rev/s . am i right? If not any hints? Cos i don't seem to get the ans.

 

[FredGarvin]

You seem to be OK. The centripital acceleration does not get influenced by the length of the cylinder. It is only a function of the radius and the angular velocity.

 

[piercas]

I would like to first commend you for taking the initiative to think critically about the proposed cylindrical habitat in space. Your approach in solving for the frequency of rotation is correct, but there are a few things to consider.

Firstly, the length of the cylinder is not mentioned in the question, so it may not be relevant in determining the frequency of rotation. However, it is important to note that the longer the cylinder, the slower the required rotation speed to simulate Earth's gravity. This is because the centrifugal force (caused by the rotation) decreases with distance from the axis of rotation.

Secondly, it is important to clarify what is meant by "imitating Earth's gravitational field at the walls of the cylinder". If it means achieving the same acceleration due to gravity (9.8 m/s^2), then your approach is correct. However, if it means simulating the feeling of gravity (i.e. experiencing a downward force), then the rotation speed needs to be adjusted to account for the Coriolis force, which can cause a feeling of weightlessness.

Lastly, your answer of 0.009043859 rev/s seems reasonable based on the given information, but it would be beneficial to double-check your calculations to ensure accuracy. Additionally, it may be helpful to provide the units for the frequency (rev/s or Hz).

In conclusion, your approach to solving for the frequency of rotation is correct, but it is important to consider the length of the cylinder and clarify the intended meaning of "imitating Earth's gravitational field" in order to determine the most accurate answer.