The Dancing Pendulum Paradox · AI Generator #GEN-997BFE9B

Physics · mechanics

Problem

A fascinating mechanical system consists of two identical uniform rods, each of mass m=0.5  kgm = 0.5\;\text{kg} and length L=1.2  mL = 1.2\;\text{m}. The first rod is pivoted at its upper end to swing freely as a physical pendulum. The second rod is initially held horizontally and positioned so that its center coincides with the lowest point of the first rod's swing path. At t=0t = 0, the first rod is released from rest at an angle θ0=60°\theta_0 = 60° from the vertical, while simultaneously the second rod is released to fall freely under gravity. Through careful observation, it is discovered that there exists a unique time t∗t^* during the motion when both rods have exactly the same angular velocity magnitude about their respective instantaneous centers of rotation. Find this special time t∗t^*. Take g=9.8  m/s2g = 9.8\;\text{m/s}^2.

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