In outer space two identical space modules are joined together by a massless cab

Question

In outer space two identical space modules are joined together by a massless cable. These modules are rotating about their center of mass, which is at the center of the cable because the modules are identical (see the drawing). In each module, the cable is connected to a motor, so that the modules can pull each other together. The initial tangential speed of each module is v0 = 17.3 m/s. Then they pull together until the distance between them is reduced by a factor of five. Each module has a final tangential speed of vf. Find the value of vf.

Explanation / Answer

from conservation of angular momentum

mvo*ro = mvf*rf

vo =17.3 m/s

rf = ro/5

17.3*ro = vf*ro/5

vf = 86.5 m/s

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