Physics help: rotational mechanics satellite

In summary: When 100 people move to the center of the station, the angular speed changes from 9.8 m/s^2 to 11.2 m/s^2. This results in an increase in total final acceleration from 0.8g to 1.6g.
  • #1
GreenLantern674
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Homework Statement


A space station shaped like a giant wheel has a radius of 90 m and a moment of inertia of 4.50 108 kg·m2. A crew of 150 are living on the rim, and the station's rotation causes the crew to experience an acceleration of 1g (Fig. P10.47). 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





The Attempt at a Solution


I've tried a couple things, including finding the rotational momentum before and after the people move and setting them equal. I did take into account the different moments of inertia and solved for them with I + MR^2, with M being the mass of the people on the outside of the station. I don't know what I'm doing wrong.
 
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  • #2
Everything you've described so far sounds correct. Show exactly what you did step by step and maybe we can spot an error.
 
  • #3
Okay, first I figured out the initial rotational velocity by using a=R(omega)^2, using 90m for R and 9.8 m/s^2 for a.
Then I figured out the total initial moment of inertia by doing I + 150(M)(R)^2
I used those to figure out the angular momentum by doing L=(I)(omega), using the I and omega I solved for above, not the given inertia.
I then set rotational momentum equal to [I<sub>given</sub> + 50(M)(R)^2] x omega and solved for omega. Then I used that omega in a=M(omega)^2 to find total final acceleration.
 
  • #4
Looks great to me. That's how I'd do it. (Are you dealing with an online system? Sometimes they are picky as to the format of the answer.)

What answers did you get for each step of your solution?
 
  • #5
Okay, I found my mistake. I just made an error adding the moments of inertia. Thanks for your help.
 

1. What is rotational mechanics?

Rotational mechanics is a branch of physics that deals with the motion and forces of objects that are rotating or moving in circular paths. It involves concepts such as torque, angular velocity, and angular acceleration.

2. How does rotational mechanics apply to satellites?

Satellites follow circular or elliptical orbits around a central body, such as the Earth. Rotational mechanics is used to understand the motion and forces acting on these satellites, including how they maintain their orbital velocity and altitude.

3. What is angular velocity?

Angular velocity is a measure of how fast an object is rotating or moving in a circular path. It is defined as the change in angular displacement over time and is measured in radians per second (rad/s).

4. What is torque?

Torque is a measure of the rotational force applied to an object. It is defined as the product of force and the perpendicular distance from the axis of rotation to the point where the force is applied. It is measured in units of Newton-meters (N-m).

5. How does the conservation of angular momentum apply to satellites?

The law of conservation of angular momentum states that the total angular momentum of a system remains constant, unless acted upon by an external torque. In the case of satellites, this means that their angular momentum, which is a product of their mass, velocity, and distance from the central body, remains constant unless external forces, such as atmospheric drag, act on the satellite.

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