Maximizing Angular Acceleration

[kitsh]

Homework Statement

A massless stick of length d, held parallel to the ground, has a mass, m, attached at one end of it and a pivot on the other end. A second mass, m, is glued on at a distance x from the pivot. At what distance x would maximize the angular acceleration of the stick the instant it is released.

Homework Equations

F=Ma
Τ=Iα=RxF
a=αR

The Attempt at a Solution

I found the center of mass position, R, to be x+(d-x)/2 and F=2mg.
With some algebra I found that Τ=2m(x+(d-x)/2)²α=2mg(x+(d-x)/2)
Then solving for α, I found α=g/(x+(d-x)/2) and to maximize I would have to take the derivative with respect to x and set it equal to zero.

I believe this work to be right but my friend brought up the fact there would be a tensile force in the stick and I don't know how that would affect the equations if it would at all.

 

[haruspex]

With some algebra I found that Τ=2m(x+(d-x)/2)²α

No, moment of inertia doesn't work like that. You cannot treat it as though both masses are at the common mass centre.
What is the standard general formula for moment of inertia?