What is the velocity of the COM of a falling rod at a given angle?

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SUMMARY

The discussion focuses on calculating the velocity of the center of mass (COM) of a falling rod at an angle θ with the horizontal. The user applies the conservation of angular momentum and the work-energy theorem to derive the equations governing the motion. However, they identify a critical error in assuming angular momentum conservation due to the presence of an external torque acting on the COM. This realization leads to the conclusion that the torque from the table must be accounted for in the analysis.

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Homework Statement


Given a rod of length 'l' placed upright on a smooth floor.A slight disturbance causes it to fall.Now required is the velocity with which the COM falls down when the rod makes angle θ with horizontal.

The Attempt at a Solution


now let the middle portion of the rod be A,and the lower portion B.Using conservation of angular momentum,we get
0=(ml^2/12)ω-m*Va*l/2*cosθ
By work energy theorem,
mgl/2*(1-sinθ)=m(Va)^2/2+ml^2/12*ω^2 (ω about point B)
What is the mistake I'm making here?
 
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Angular momentum is not conserved. The table has a torque on the COM of the rod, meaning there is an external force which has a torque.
 

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