You are pulling on a rope attached to the outer radius of a pulley with a moment of inertia I=8.34 kg⋅m2 as shown. The magnitude of the tension force of you on the pulley is 539.7 N. A pack of mass 38.6 kg is attached to the pulley's inner radius as shown. If the inner radius of the pulley is 0.52 m and the outer radius is 0.65 m, what is the magnitude of the linear acceleration of the pack?

You are pulling on a rope attached to the outer radius of a pulley with a moment of inertia I=8.34 kg⋅m2 as shown. The magnitude of the tension force of you on the pulley is 539.7 N. A pack of mass 38.6 kg is attached to the pulley's inner radius as shown. If the inner radius of the pulley is 0.52 m and the outer radius is 0.65 m, what is the magnitude of the linear acceleration of the pack?