Two radii pulley lifting a pack

[getty102]

Homework Statement

You are pulling on a rope attached to the outer radius of a pulley with a moment of inertia I=676 kgm2 as shown. The tension in the rope that you are pulling is 477.9 N. A pack of mass 30.8 kg is attached to the pulley's inner radius as shown. If the inner radius of the pulley is 0.56 m and the outer radius is 0.8 m, what is the magnitude of the linear acceleration of the pack?

Homework Equations

Ʃtorque=(I)(\alpha)
ƩF=ma

The Attempt at a Solution

I found the tension due to the mass of the pack on the pulley.
T_ps=m_p(g-a_t)
p=pack, a_t=linear acceleration of pack

I then summed the torques, and inserted the tension due to the pack on the pulley
R(T_yr)-r(m_p(g-a_t))=I(a_t/R)

solved for a_t=[R(T_yr)-r(m_p*g)]/[(I/R)-(r*m_p)]

my final a_t=24.233 m/s/s which is not right

 

[gneill]

You might want to check your expression for T_ps. Make sure that the implied forces result in an acceleration in the desired direction for the pack.