Pulley problem with moment of inertia

[howsockgothap]

Homework Statement

A 28.5 kg block (m1) is on a horizontal surface, connected to a 6.10 kg block (m2) by a massless string. The frictionless pulley has a s R = 0.087 m and a moment of inertia I=0.140 kgm2. A force F = 231.3 N acts on m1 at an angle theta = 30.5°. There is no friction between m1 and the surface. What is the upward acceleration of m2?

m2 is hanging off a pulley that's attached to the end of the surface as m1 is dragged across the surface by force F

Homework Equations

f=ma
I=?

The Attempt at a Solution

Initially I tried ignoring the moment of inertia and solving with just tensions but obviously that is not possible. My main problem is that (as you can see from part 2) I am not sure what equation I should be using in reference to the pulley's moment of inertia.

 

[Hootenanny]

Homework Statement

A 28.5 kg block (m1) is on a horizontal surface, connected to a 6.10 kg block (m2) by a massless string. The frictionless pulley has a s R = 0.087 m and a moment of inertia I=0.140 kgm2. A force F = 231.3 N acts on m1 at an angle theta = 30.5°. There is no friction between m1 and the surface. What is the upward acceleration of m2?

m2 is hanging off a pulley that's attached to the end of the surface as m1 is dragged across the surface by force F

Homework Equations

f=ma
I=?

The Attempt at a Solution

Initially I tried ignoring the moment of inertia and solving with just tensions but obviously that is not possible. My main problem is that (as you can see from part 2) I am not sure what equation I should be using in reference to the pulley's moment of inertia.

You have correctly identified that you need to use Newton's second law for linear accelerations. What you now need to Newton's second low for Rotations - see: http://hyperphysics.phy-astr.gsu.edu/hbase/n2r.html