a rod of length L, whose lower end is resting along the horizontal plane, starts to topple from the vertical position.what will be the velocity of upper end when it hits the ground?
i think it will be ± 2√5.√L
square root(3gl)
it appears from your question that the rod is falling in such a way that it is in pure rotation about its lower end which is in contact with the horizontal plane.
see you can easily realize that when the rod is falling in such a situation then the floor must be sufficiently rough to prevent sliding of the lower end.
in case it were a smooth floor then the rod would fall but the lower end will definitely slide along the floor because the center of mass has to fall vertically only because there is no net force along the horizontal direction.
so i am posting the solution for the first situation feeling that the the rod TOPPLES.
(1/2)*(1/3)ML2w2 = MgL/2
this gives w = (3g/L)(1/2).
so the velocity of the upper end is Lw = (3gL)(1/2).
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