Combining Newton's Laws: Solving for Acceleration and Moment of Inertia

[Alkatran]

I have the following problem that I can't seem to solve.

Combine these two equations:
TR = I(alpha) *Newton's 2nd law of Rotation for the wheel
T - mg = ma *Newton's Second law for the mass
to make this one:
mg = I/R^2*a

Note that a is much smaller than g

I break it to:

mg = I(alpha)/r - ma or I(alpha)/r ... unless (alpha) = a/r in which case ... hmmm

First of all I notice that alpha and T are eliminated. Two variables gone for two equations?? (a is smaller than g, does that mean alpha is...?)

Also, where does R^2 come from?

I think T if force (F), R is radius (r)
I is moment of inertia, alpha is angular accel, m is mass, g is (duh) gravitational constant and a should be acceleration

 

[PrudensOptimus]

I couldn't remember what "I" is defined as in terms of algebraic expression.

But "R^2" comes from a_centripedal = v^2/r = alpha; after you combine

mg = ma - Ialpha/r, you plug in v^2/r for alpha, you get /r^2