Pulley problem with moment of inetia

[Iansno1]

Problem

As shown below, Block A has mass 'M' and rests on a surface with a coefficient of kinetic friction 'U_k' .The cord attached to A passes over a pulley at C and is attached to a block B of mass '2M'. If B is released calculate the acceleration of A.

Assume the cord does not slip over the pulley. The Pulley can be approximated as a thin disk of radius 'r' and mass 'M/4' . Neglect the mass of the cord
Relevant equations

moment of inertia of the disk: I=0.5*M*r²
Not sure where to start

 

[ehild]

with free body diagrams?

ehild

 

[Iansno1]

How does the Moment of inertia come into the equation? I can do these problems when the pulley is assumed to have no mass and no friction.

 

[gneill]

How does the Moment of inertia come into the equation? I can do these problems when the pulley is assumed to have no mass and no friction.

Moment of inertia is the analog of mass for rotational motion. The moment of inertia resists angular acceleration in the same fashion as mass resists linear acceleration.

In this problem the pulley adds resistance to the acceleration of the overall system because the cord does not slip, and so must cause angular acceleration of the pulley. The angular acceleration is related to the linear acceleration (how?).