Gravitational Field Strength of Space Station w/ N Astronauts

[fizics]

Homework Statement

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?

Homework Equations

mrw^2=mg

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.

 

[LowlyPion]

Welcome to PF.

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

 

[fizics]

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

 

[heth]

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

 

[fizics]

kinetic energy?

 

[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'?

 

[fizics]

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

 

[LowlyPion]

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

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

 

[fizics]

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

 

[heth]

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

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

 

[fizics]

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