Answer to Question #280090 in Physics for Faith

Question

A space station consists of two donut-shaped living chambers, A and B, that have the radii shown in the figure. As the station rotates, an astronaut in chamber A is moved 236 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time if r_a = 463 m and r_b = 493 m?

Answer 1

$$S=s\frac{R}{r}\\S=236\frac{493}{463}=251\ m$$