Pulley System: Acceleration & Angular Acceleration

AI Thread Summary
In a frictionless pulley system with a mass ratio of 1:4, the acceleration of the blocks can be determined by analyzing the forces acting on each mass. The tension in the ropes, T_1 and T_2, along with the gravitational forces, are essential for calculating the net force and resulting acceleration. The angular acceleration of the pulley is linked to the linear acceleration of the masses through the radius of the pulley. A free body diagram is crucial for visualizing the forces and deriving the equations needed to solve for both accelerations. Understanding these relationships is key to solving the problem effectively.
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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

 
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Show some attempt to solve.
 
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
 

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