An astronaut floating in deep space far from any celestial body can be modeled as a…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
An astronaut floating in deep space far from any celestial body can be modeled as a uniform cylinder of mass 80kg and radius 0.25m. The astronaut is initially rotating at 0.50rad/s about her central axis while holding a 2.0kg wrench in an outstretched hand at an arm’s length of 1.0m from the axis. At a certain instant she releases the wrench so that it moves tangentially outward and eventually drifts away without further interaction. Neglect external torques on the astronaut–wrench system.
(a) Derive an algebraic expression for the astronaut’s angular speed ωa immediately after the wrench is released, expressing your result in terms of known quantities.
(b) Calculate the numerical value of ωa using the given data.
(c) Determine the linear speed of the wrench relative to an inertial reference frame immediately after release.
(d) Evaluate the change in rotational kinetic energy of the astronaut–wrench system between times just before and just after the release, and discuss the physical process responsible for this change.