Conservation of angular momentum of space station

[olso4142]

[SOLVED] Conservation of angular momentum

A space station shaped like a giant wheel has a radius of 1.00x10E2 m and a moment of inertia of 5.00x10E8 kgm2. A crew live on the rim and the staion is rotaing so that the crew experiences an apparent acceleration of 1g (1x9.81m/s2). When 120 people move to the center of the station for a union meeting, the angular speed changes. What apparent acceleration is experienced by the managers at the rim? Assume the average mass of a crew member is 65.0kg.



2. I think u have to use Li=Lf which is IiWi=IfWf
I=mr2 because its a disk




3. IiWi=IfWf(the group on the rim)+If2Wf2(group at the center)
the group at the centers r=0 so I=0 so that is eliminated
m(total)r2Wi=m(rim)r2Wf
I put in my masses and my radius and solved for Wi=1/5Wf

don't know what to do know or if that is even right please help!

 

[rl.bhat]

From the given data find the mass and velocity ( using m*v^2/r = g) of the space station. Using Wi=1/5Wf find the final velocity. From that find apparent g.

 

[ogb p]

I can confirm that the conservation of angular momentum is a fundamental principle in physics. This means that the total angular momentum of a system remains constant unless acted upon by an external torque. In the case of the rotating space station, the moment of inertia and the angular velocity are directly proportional, so any change in one will result in a change in the other to maintain the same angular momentum.

In this scenario, when the 120 people move to the center of the station, the moment of inertia decreases. This means that in order to maintain the same angular momentum, the angular velocity must increase. However, the apparent acceleration experienced by the managers at the rim will not change, as it is determined by the radius and the angular velocity, not the moment of inertia.

Using the equation IiWi=IfWf, we can solve for the new angular velocity (Wf) of the managers at the rim, which is 1/5 of the original angular velocity (Wi). This means that the apparent acceleration experienced by the managers at the rim will also be 1/5 of the original value, which is still 1g (9.81m/s^2).

In conclusion, the conservation of angular momentum is a crucial concept to understand in this scenario, as it explains why the apparent acceleration experienced by the managers at the rim remains constant despite the change in the distribution of mass on the space station.