# Space station problem

1. Nov 17, 2008

### sweedeljoseph

1. The problem statement, all variables and given/known data
A space station consists of two doughnut shaped living chambers, A and B, that have the radii shown in the drawing. As the station rotates, an astronaut in chamber A is moved 2.40 x 102 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time?

here is the picture for more reference:
http://img407.imageshack.us/img407/2496/picgr3.jpg

2. Relevant equations
i dont know if these will help we just got alot today so here:
w=$$\theta$$/Delta t
*v=vo+at ~ w=wo+$$\omega$$t
*v2=vo2+2ax ~ w2=wo2+2$$\omega$$$$\theta$$
*x=vot+(1/2)at2 ~ $$\theta$$=wot+(1/2)at2

the ones with * means i changed it to what the problem is about. means the same thing just different letters so you wont get confused i guess.

3. The attempt at a solution
i have no idea what im supposed to do. i know the arc length should be the same as the radius because its has something to do with radians? i have no clue what im supposed to do. please help me.

thank you!
sweedeljoseph

2. Nov 17, 2008

### tiny-tim

Hi sweedeljoseph!

arc-length = rθ

(so the arc-length equals the radius only if the arc-angle is 1 radian!)

3. Nov 17, 2008

### sweedeljoseph

how would i know if the angle is 1 radian?

4. Nov 17, 2008

### tiny-tim

5. Nov 17, 2008

### sweedeljoseph

i know that but how do you know from the problem what the angles are?

6. Nov 18, 2008

### tiny-tim

Hi sweedeljoseph!

This is a very simple symmetry problem (expansional symmetry ) …

the space station is rigid, so if A goes 240m round a circle of radius 320m, then B goes … round a circle of radius 1100m?

7. Nov 18, 2008

### sweedeljoseph

yea...
my teacher showed me how to do this today. i feel so stupid. haha.

thank you though!
sweedeljoseph