Rotational Inertia problem: Getting different results from two solving methods

[mg11]

Homework Statement

A disk of radius r meters has a string wrapped around its perimeter. A mass of m kilograms is attached to the end of the string and is allowed to descend freely from a height of h meters, it takes t seconds for the mass to travel the distance.

Find the moment of inertia (I) for the disk.

Homework Equations

Dynamic principles:
Torque = r*mg
Torque = I*Alpha

Energy principles:
G.P.E = m * g * h {G.P.E: Gravitational Potential Energy}
KT = 1/2 * m * v^2 {KT: Translational (linear) Kinetic Energy}
KR = 1/2 * I * w^2 {KR: Rotational Kinetic Energy, w: Omega (angular velocity)}

The Attempt at a Solution

I'm trying to solve this problem using both methods (energy principles and dynamic principles) and I'm getting different results.

Using energy principles I get:

I = m * r^2 * [(g * t^2 / 2*h) - 1]

Using dynamic principles I get:

I = (t^2 * r^2 * m * g) / (2 * h)Why am I getting different expressions?

Thanks!

 

[Doc Al]

Dynamic principles:
Torque = r*mg

Do not assume that the tension in the string, which is what provides the torque on the disk, is equal to the weight of the hanging mass. (If it were, then the mass would be in equilibrium.) Solve for the tension.

 

[mg11]

Yep... makes sense and works great, thank you!