Question

A space station consists of two donut-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 2.30 102 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time?

Answer 1

The angle subtended by the arc of movement of both chambers is the same. Thus:
S = r∅, for chamber A:

2.3 x 10² = 3.2 x 10² ∅
∅ = 0.72 rad

∅ is the same for B so:
S = 1.1 x 10³ x 0.72
S = 7.92 x 10² m