Why Can't I Use Torque = Ia for Calculating Pulley's Inertia?

[kp]

once again I have succeeded in confusing myself about basic angular motion...

If I have a pulley of with an unkown moment of inertia, and a bucket hanging from the pulley with a known mass, height, and acceleration in which it falls. Why can't i use:

Torque = Ia
rf = Ia
r * mg = Ia
r*mg/a = I

or can I, because when i use conservation of energy

mgh = 1/2mv^2 + 1/2Iw^2 and solve for I, i get different answers.

 

[Doc Al]

Torque = Ia
rf = Ia
r * mg = Ia
r*mg/a = I

This assumes that the force exerted on the pulley equals the weight of the hanging mass. Not true. The force does equal the tension in the cord. (If the force exerted on the pulley equalled the weight of the hanging mass, then by Newton's 3rd law the mass would be in equilibrium.)