(1) in the case of ice, the iron rod spins around the center of mass while it falls,

the initial rate of change of the angular velocity (d(omega)/dt)= moment of force/moment of inertia of rotation (I_1),

I_1=moment around the axis passing the center of mass.

(2) In the case of one end fixed on the ground, the rod spis around the fixed end,

d(omega)/dt=moment of force/moment of inertia of rotation (I_2)

I_2=moment around the fixed end.

I_2>I_1. The moment of force in 1) comes from the upward force at the ice contact point. This force can be assumed to be equal to m*g for very small t. There is something murky here, but let's assume F=mg, then the force moments in the two cases are equal, so

d(omega)/dt for case 1 > d(omega)/dt for case 2.