The motion of a spring released from uniform circular motion

Abstract

A weak spring is connected to the end of a rotor rotating at constant angular velocity. The spring extends to a stretched length as determined by the spring mass, rest length, spring constant, rotor radius, and rotor angular velocity. When released from the rotor, captured video shows the inner end of the spring pulling away as expected, causing a wave to travel down the spring as it collapses. During this collapse, the outer end of the spring continues to move along its original circular path in uniform circular motion, as if the spring were still connected to the rotor. Values from a numerical model and measurements from video analysis show that after release the inner end travels along a circle of similar radius as the outer end. Simulation results are presented that agree with the video analysis.