# Space station

1. Dec 12, 2008

### fizics

1. The problem statement, all variables and given/known data
A space station consists of two living modules attached to a central hub on opposite sides of the hub by long corridors of equal length. Each living module contains N astronauts of equal mass. The mass of the space station is negligible compared to the mass of the astronauts, and the size of the central hub and living modules is negligible compared to the length of the corridors. At the beginning of the day, the space station is rotating so that the astronauts feel as if they are in a gravitational field of strength g. Two astronauts, one from each module, climb into the central hub, and the remaining astronauts now feel a gravitational field of strength g′. What is the ratio g/g′ in terms of N?
2. Relevant equations
mrw^2=mg

3. The attempt at a solution
I can go no further after calculating the new rotational inertia.I don't know how the angular velocity would change.

Last edited: Dec 13, 2008
2. Dec 12, 2008

### LowlyPion

Welcome to PF.

How do you think you should approach the problem(s).

3. Dec 12, 2008

### fizics

I can go no further after calculating the new rotational inertia.I don't know how the angular velocity would change.

4. Dec 13, 2008

### heth

A lot of problems involve conservation of physical quantities. What might be conserved here?

5. Dec 13, 2008

### fizics

kinetic energy?

6. Dec 13, 2008

### LowlyPion

What is the formula for rotational kinetic energy?

You have the new moment of inertia. So ... don't you have a way to figure the new kinetic energy and hence the new force g'?

7. Dec 13, 2008

### fizics

Thank you.But I would like to know what is unchanged in the problem.Is the angular velocity unchanged?

8. Dec 13, 2008

### LowlyPion

The rotational kinetic energy is unchanged isn't it?

KE = ½Iω² = ½Iv²/r

If you change I and KE is constant ...

v² = 2*KE*r/I

and new g = v²/r = 2*KE*/I

9. Dec 13, 2008

### fizics

OK,thx,and is angular momentum conserved here?Because the system of the station of astronauts is isolated.

10. Dec 13, 2008

### heth

What's your gut feeling? Do you think it would be conserved, or wouldn't be conserved?

11. Dec 13, 2008

### fizics

I think the angular momentum of the system(people and station) is conserved.