Read the previous post first

Here's another example

In this question, you need to find out the angular acceleration of the pulley.
I'll use torque=moment of inertia*angular acceleration in a differente' fashion.

Write the torque about 'P' (the center of rotation is ALWAYS denoted by the letter 'P'):
Torque=m1*g*R-m2*g*R

Now whats the moment of inertia about 'P'? The rigid body contributes M*(K^2). But how much MOI do the masses 'm1' and 'm2' contribute? m1 contributes m1*(R^2). m2 contributes m2*(R^2).

Now, we write:
m1*g*R-m2*g*R=(M*(K^2)+ m1*(R^2)+m2*(R^2))*alpha.

Now find alpha.