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 1.50 x 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

To find out how far along a circular arc an astronaut in chamber B is moved during the same time, we must first find the ratio of the radii of chambers A and B.

From the figure, we see that the radius of chamber A (rA) is 5 times smaller than the radius of chamber B (rB):
rA : rB = 1 : 5

Now, we can say that:

arc_lengthA / arc_lengthB = rA / rB

Given that the astronaut in chamber A is moved 1.50 x 10^2 m along a circular arc, we can plug the values into the equation and solve for arc_lengthB:

(1.50 x 10^2) / arc_lengthB = 1 / 5

To solve for arc_lengthB, we multiply both sides by 5, and we get:

arc_lengthB = 5 * (1.50 x 10^2)

arc_lengthB = 7.5 x 10^2 m

So, during the same time, an astronaut in chamber B is moved 7.5 x 10^2 meters along a circular arc.