Pulley problem with moment of inetia

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Homework Help Overview

The problem involves a system with two blocks connected by a cord over a pulley, where one block is affected by friction. The pulley has mass and a moment of inertia, which complicates the calculation of acceleration for the blocks. Participants are exploring the dynamics of the system, particularly how the moment of inertia of the pulley influences the overall motion.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the use of free body diagrams to analyze the forces acting on the blocks and the pulley. There are questions about how to incorporate the moment of inertia into the equations of motion, particularly in relation to the angular acceleration of the pulley and its effect on the linear acceleration of the blocks.

Discussion Status

The discussion is ongoing, with participants raising questions about the role of the moment of inertia in the problem. Some have expressed uncertainty about how to start the analysis, while others are attempting to clarify the relationship between linear and angular acceleration in the context of the pulley system.

Contextual Notes

Participants are working under the assumption that the cord does not slip over the pulley and that the mass of the cord is negligible. There is a focus on understanding the implications of the pulley having mass and friction, which is different from simpler problems where the pulley is considered massless.

Iansno1
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Problem

As shown below, Block A has mass 'M' and rests on a surface with a coefficient of kinetic friction 'Uk' .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
 

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with free body diagrams?

ehild
 
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.
 
Iansno1 said:
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?).
 

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