Pulley System: Acceleration & Angular Acceleration

[kashhustler]

Homework Statement

Given a frictionless pulley system with the pulley having a mass 1/3M and radius R, and two weights of mass M and 4M attached to a light, frictionless rope on either side of the pulley:

1) Find the acceleration of the blocks

2) Find the angular acceleration of the pulley

Homework Equations

The Attempt at a Solution

 

[Shooting Star]

Show some attempt to solve.

 

[Bill Foster]

Start with a free body diagram and label the forces involved.

The forces on the mass M are:

$$T_1$$ (tension in rope connected to the mass)
$$-gM$$

The forces on the mass 4M are:

$$T_2$$ (tension in rope connected to the mass)
$$-g4M$$