Question

6.) 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 1.59 10² m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time? $08_10.gif$

Answer 1

Radius of chamber A = R_A = 3.2 x 10² m

Radius of chamber B = R_B = 1.1 x 10³ m

Distance an astronaut in chamber A moves along a circular arc = L₁ = 1.59 x 10² m

Angle through which the chamber A rotates = $\theta$ ₁

L₁ = R_A$\theta$₁

1.59x10² = (3.2x10²)$\theta$₁

$\theta$₁ = 0.497 rad

Distance an astronaut in chamber B moves along a circular arc in the same time = L₂

Angle through which the chamber B rotates in the same time = $\theta$ ₂

The angle through which both the chambers rotate in the same time is equal.

$\theta$₁ = $\theta$ ₂

$\theta$₂ = 0.497 rad

L₂ = R_B$\theta$₂

L₂ = (1.1x10³)(0.497)

L₂ = 5.47 x 10² m

Distance an astronaut in chamber B moves along a circular arc in the same time = 5.47 x 10² m