Please explain the solution....a metre long rod is kept vertically and allowed to fall the ground.if the lower end does not slip ,find the velocity of the upper end when it strikes the ground

Use conservation of energy principle. PE lost by the rod is converted into the KE of the rod.

Initial PE of the rod = 1/2.MgL

Final K.E. = Rot.KE. about the lower end = 1/2.I(omega)^2 = 1/2.(1/3ML^2).(omega)^2

Equate the two to get omega and next,

Vel of the upper end = (omega).L and its direction is vertically downwards.

How did you equate the potential energy of the centre of mass of the rod to the total rotational kinetic energy of the whole rod...what is the logic???please explain..