Space Station - Conservation of Angular Momentum

In summary, the conversation discusses a space station shaped like a giant wheel with a radius of 109m and a moment of inertia of 5.07x10^8 kgm^2. The station is rotating to create an apparent acceleration of .8g for the crew of 180 living on the rim. When 140 people move to the center, the angular speed changes and the managers remaining at the rim experience an apparent acceleration of 1.15g. This is found using the equation Ar` = [(I + NmR^2) * Root (Ar*R) / R] / (I + N`mR^2).
  • #1
moo5003
207
0
Question:

A space station shaped like a giant wheel has a radius 109m and a moment of inertia of 5.07x10^8 kgm^2. A crew of 180 is living on the rim, and the station is rotating so that the crew experiences an apparent acceleration of .8g. When 140 people move to the center of the station for a union meeting, the angular speed changes. What apparent acceleration is experienced by the managers remaining at the rim? Assume an average mass of 64.0 kg for all the inhabitants.

What I have done thus far:
I = 5.07x10^8
N = 180
N`= 40
m = 64.0
A = .8

L = L`
L = (I + NmR^2)w
L` = (I + N`mR^2)w`

w' = [(I + NmR^2)w] / (I + N`mR^2)

Problem: How do I solve for radial acceleration, when I do not even have the radial speed or the initial speed.

W = Initial + AT ---- Are they asking for radial acceleration or the force felt pushing the inhabitants down on the rim.
Any help is appreciated.
 
Last edited:
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  • #2
Alright I solved it

Basically I did the following:

Acceleration is the centrifugal force with is equal in magnitude to the centripital force.

Ar = V^2 / 2
V = Root (Ar*R)
w = Root (Ar*R) / R

Substuting that for w` and w I arrived at the equation

Ar` = [([(I + NmR^2) * Root (Ar*R) / R] / (I + N`mR^2)) R ] ^2 / R
Ar` = 1.15g Can anyone double check for me.
 
  • #3
Check. I got 1.148g
 

Related to Space Station - Conservation of Angular Momentum

1. What is the Space Station and why is it important?

The Space Station is a large spacecraft that orbits around the Earth. It is important because it serves as a research laboratory for scientists to conduct experiments in microgravity, study the effects of space on humans, and test new technologies for future space exploration.

2. How does conservation of angular momentum apply to the Space Station?

Conservation of angular momentum is a fundamental principle in physics that states that an object will continue to spin at a constant rate unless acted upon by an external force. In the case of the Space Station, conservation of angular momentum is crucial for maintaining its orbit around the Earth. The Station's large solar panels and other equipment are carefully positioned to distribute its mass evenly, ensuring that it stays in a stable orbit without the need for constant adjustments.

3. How is the Space Station kept in orbit?

The Space Station is kept in orbit by the force of gravity. The Earth's gravitational pull keeps the Station in a constant state of freefall, causing it to continuously orbit around the planet. The Station's speed and altitude are carefully calculated to maintain this orbit, and occasional boosts from spacecraft are necessary to counteract any atmospheric drag.

4. What are some challenges faced in maintaining the Space Station's orbit?

One of the main challenges in maintaining the Space Station's orbit is dealing with atmospheric drag. The Earth's atmosphere is not completely uniform, and at higher altitudes where the Station orbits, there is still enough resistance to slow it down. This requires periodic boosts from spacecraft to maintain the Station's orbital velocity. Additionally, the Station's orbit must also be carefully monitored and adjusted to avoid collisions with other space debris.

5. How is conservation of angular momentum important for future space missions?

Conservation of angular momentum is crucial for future space missions as it allows spacecraft and other objects to maintain their orientation and trajectory without the need for constant adjustments. This is especially important for long-term missions, such as deep space exploration, where resources and communication with Earth are limited. By carefully designing spacecraft and equipment to distribute their mass and maintain a stable spin, conservation of angular momentum can help ensure the success of future space missions.

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