Artificial gravity is a must for any space station if humans are to live there for any extended length of time. Without artificial gravity, human growth is stunted and biological functions break down. An effective way to create artificial gravity is through the use of a rotating enclosed cylinder, as shown in the figure. Humans walk on the inside of the outer edge of the cylinder, which has a diameter of D = 2035 m that is large enough such that its curvature is not readily noticeable to the inhabitants. (The space station in the figure is not drawn to scale.) Once the space station is rotating at the necessary angular speed w to create an artificial gravity of 1 g, how many minutes would it take the space station to make one revolution? revolution: minutes D 13
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![Artificial gravity is a must for any space station if humans are to live there for any extended length of time. Without artificial gravity, human growth is stunted and biological functions break down.
An effective way to create artificial gravity is through the use of a rotating enclosed cylinder, as shown in the figure. Humans walk on the inside of the outer edge of the cylinder, which has a diameter of \( D = 2035 \, \text{m} \) that is large enough such that its curvature is not readily noticeable to the inhabitants. (The space station in the figure is not drawn to scale.)
Once the space station is rotating at the necessary angular speed \( \omega \) to create an artificial gravity of 1 g, how many minutes would it take the space station to make one revolution?
Diagram Explanation:
- The diagram depicts a rotating circular cylinder representing the space station.
- The arrow labeled \( \omega \) indicates the direction of rotation.
- The diameter of the cylinder is marked as \( D \), which is 2035 meters.
- A human figure is shown standing on the inner surface of the cylinder, illustrating the concept of artificial gravity through rotation.
A text box labeled "revolution:" is provided for input in minutes to determine how long it takes for the space station to complete one revolution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52caa5b4-58c6-470e-a25b-6f2dba4e23c8%2F66e9e85c-bf64-48a2-bcde-47ee61550513%2Fkzygutn_processed.png&w=3840&q=75)
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