Solving a Frictionless Pulley Problem: Acceleration of m2

[physicsbro]

Homework Statement

A 29.3 kg block, m1, is on a horizontal surface, connected to a 6.70 kg block, m2, by a massless string as shown. The frictionless pulley has a radius R = 0.055 m and a moment of inertia I = 0.100 kg·m2. A force F = 202.5 N acts on m1 at an angle θ = 29.7°. There is no friction between m1 and the surface. What is the upward acceleration of m2?

Homework Equations

The Attempt at a Solution

My textbook says that the net tension divided by the moment of inertia would give me the \alpha and that multiplied by the radius would give me the acceleration, but it didnt work.

 

[Doc Al]

My textbook says that the net tension divided by the moment of inertia would give me the \alpha and that multiplied by the radius would give me the acceleration, but it didnt work.

That's certainly true, but you'll need the tensions to make use of it. Hint: Apply Newton's 2nd law to both masses and the pulley. Combine those three equations and you can solve for the acceleration.