A thin horizontal uniform rod AB of mass m and length l can rotate freely about a vertical axis passing through its end A. At a certain moment, the end B starts experiencing a constant force F which is always perpendicular to the original position of the stationary rod and directed in a horizontal plane. Find the angular Velocity of the rod as a function of its rotation angle θ measured relative to the initial position

Question

A thin horizontal uniform rod AB of mass m and length l  can rotate freely about a vertical axis passing through its end A. At a certain moment, the end B starts experiencing a constant force F which is always perpendicular to the original position of the stationary rod and directed in a horizontal plane. Find the angular Velocity of the rod as a function of its rotation angle θ measured relative to the initial position

Infinity Learn · Accepted Answer

Work done by the torque Δ$$w=$$∫Tdθ$$=$$∫$$0$$θFlcosθdθΔ$$w=Fl$$ $$sin$$θNew using work energy theoryΔ$$w=$$ΔkFlsinθ$$=12ml23$$ω$$2$$−$$0$$ω$$=6Fsin$$θml

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