The Wobbling Space Station · AI Generator #GEN-134A2480

Physics · mechanics

Problem

A cylindrical space station of radius

R = 100\;\text{m}

and mass

M = 2.0 \times 10^6\;\text{kg}

rotates about its central axis to provide artificial gravity. The station's moment of inertia about its rotation axis is

I = \frac{1}{2}MR^2

. Initially, the station rotates at angular velocity

\omega_0 = 0.20\;\text{rad/s}

. Due to a malfunction, a large cargo pod of mass

m = 1.0 \times 10^4\;\text{kg}

breaks free from the station's outer rim and slides radially inward along a frictionless track. The pod was initially at rest relative to the station's surface. Find the station's angular velocity when the cargo pod reaches a distance of

r = 50\;\text{m}

from the center.

Browse the problem library