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. The angular velocity of the rod as a function of its rotation angle θ measured relative to the initial position should be

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. The angular velocity of the rod as a function of its rotation angle θ measured relative to the initial position should be

Infinity Learn · Accepted Answer

Work done by the torque∆W $$=$$ ∫τdθ  $$=$$ ∫$$0$$θFl $$cos$$ θ dθ∆W $$=$$ Fl $$sin$$ θNow using work energy theorem,∆W $$=$$ ∆k∴ Flsinθ $$=$$ [$$12(ml23)$$ω$$2-0$$]Which gives, ω $$=$$ $$6F$$ $$sin$$ θml

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