Space station living quarters problem

[sweedeljoseph]

Homework Statement

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

Homework Equations

i don't know if these will help we just got a lot today so here:
w=$$\theta$$/Delta t
*v=v_o+at ~ w=w_o+$$\omega$$t
*v²=v_o²+2ax ~ w²=w_o²+2$$\omega$$$$\theta$$
*x=v_ot+(1/2)at² ~ $$\theta$$=w_ot+(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 won't get confused i guess.

The Attempt at a Solution

i have no idea what I am 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 I am supposed to do. please help me.

thank you!
sweedeljoseph

 

[tiny-tim]

i know the arc length should be the same as the radius because its has something to do with radians?

Hi sweedeljoseph!

Arc-length = radius times angle (with angle measured in radians):

arc-length = rθ ​

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

 

[sweedeljoseph]

how would i know if the angle is 1 radian?

 

[tiny-tim]

how would i know if the angle is 1 radian?

2π radians is 360º

so 1 radian = (180/π)º.

 

[sweedeljoseph]

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

 

[tiny-tim]

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?

Hi sweedeljoseph!

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

you don't need to know anything about angles or radians …

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?

 

[sweedeljoseph]

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

thank you though!
sweedeljoseph