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A bola consists of three massive, identical spheres connected to a common point by identical lengths of sturdy string.

A bola consists of three massive, identical spheres connected to a common point by identical lengths of sturdy string. To launch this native South American weapon, you hold one of the spheres overhead and then rotate that hand about its wrist so as to rotate the other two spheres in a horizontal path about the hand. Once you manage sufficient rotation, you cast the weapon at a target. Initially the bola rotates around the previously held sphere at angular speed ωi but then quickly changes so that the spheres rotate around the common connection point at angular speed ωf, as seen in the figure below. (For the following questions, approximate the spheres as having all their mass located at their centers.)

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