A cylindrical space habitat of radius rotates in deep space to provide its occupants…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A cylindrical space habitat of radius 150m rotates in deep space to provide its occupants with an apparent gravitational acceleration of 9.8m/s2 at the interior surface. An astronaut standing on the inside wall begins walking in the direction opposite to the habitat’s rotation at a steady speed of 2.0m/s relative to the surface.
Engineers wish to understand both the motion of the habitat itself and the motion of the astronaut relative to an inertial frame.
(a) For predicting the artificial gravity experienced by stationary equipment bolted to the interior wall, state whether the habitat should be modeled as a single object or as a rigid system. Explain your reasoning.
(b) For analysing changes in the habitat’s rotation rate caused by the astronaut’s walk, decide how the habitat–astronaut combination should be modeled. Justify your answer, identifying which parts of the system must be treated as rigid bodies and which can be approximated as single particles.
(c) Derive an expression for the new rotation rate of the habitat after the astronaut has reached a speed v relative to the surface, in terms of the initial rotation rate, the masses of the habitat and astronaut, and other relevant geometric parameters. State clearly any additional assumptions you make.
(d) Discuss qualitatively how ignoring the astronaut’s internal rotation (for example, arm-swing) affects the accuracy of the prediction from part (c).