Find the acceleration of a space station

In summary, the problem involves a space station shaped like a giant wheel with a radius of 98 m and a moment of inertia of 4.95 x 10^8 kg*m^2. The station is rotating at a speed that creates an apparent acceleration of 1g for the crew of 150 living on the rim. When 100 people move to the center of the station, the angular speed changes and the remaining managers on the rim experience a different acceleration. The first step is to calculate the angular speed of the station using the equation ω=sqrt(g/r), and then use the mass of the inhabitants to calculate the angular momentum and kinetic energy. From there, conservation of quantities can be used to solve for the acceleration
  • #1
cabiggs22
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Homework Statement


A space station shaped like a giant wheel has a radius 98 m and a moment of inertia of 4.95 108 kg · m2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1g. When 100 people move to the center of the station for a union meeting, the angular speed changes. What acceleration is experienced by the managers remaining at the rim? Assume that the average mass of each inhabitant is 65.0 kg.


Homework Equations


I=MR^2
τ=Iα=rF
g=rω^2


The Attempt at a Solution

 
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  • #2
What part of this problem are you having trouble doing? The first part should be figuring out how fast the station is rotating, and then using that information and the mass of the inhabitants to calculate the angular momentum/angular kinetic energy of the ship. From there, figure out what quantities are conserved.
 
  • #3
I might be really stupid (I'm definitely not a physics person!), but I just don't understand anything of what I am doing... Do I just make ω=sqrt(g/r) and then what?
 

1. What is the definition of acceleration?

Acceleration is the rate of change of an object's velocity over time. It is measured in meters per second squared (m/s²).

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. How is acceleration related to the motion of the space station?

The acceleration of a space station is directly related to its motion. If the space station is speeding up, its acceleration will be positive. If the space station is slowing down, its acceleration will be negative. If the space station is moving at a constant speed, its acceleration will be zero.

4. What factors affect the acceleration of a space station?

The acceleration of a space station can be affected by various factors such as the thrust of its engines, the force of gravity, and any external forces acting on the station. Other factors like air resistance and friction can also impact the acceleration of a space station.

5. How is the acceleration of a space station useful?

The acceleration of a space station is useful for understanding its motion and predicting its future trajectory. It is also important for ensuring the safety and stability of the space station and its occupants. Additionally, knowledge of acceleration can help in planning and executing maneuvers and experiments on the space station.

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