What is the Moment of Inertia of a Pulley with Connected Masses?

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Homework Help Overview

The problem involves a pulley system with two connected masses, where one mass slides on a smooth surface and the other is hanging. The objective is to determine the moment of inertia of the pulley, given specific parameters such as mass values and acceleration.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the implications of a massless pulley on the system's acceleration and how to account for differences in acceleration due to the pulley’s mass. There are suggestions to analyze the system using Free Body Diagrams and to write equations of motion for both masses and the pulley.

Discussion Status

The discussion is ongoing, with participants offering hints and guidance on how to approach the problem. There is a focus on understanding the forces at play and the relationships between linear and rotational motion. No consensus has been reached, but several productive lines of inquiry have been suggested.

Contextual Notes

Participants note the absence of references in the original poster's textbook regarding this type of problem, indicating a potential gap in foundational knowledge that may affect the discussion.

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Homework Statement


A mass (M1 = 5.0 kg) is connected by a light rope to a mass (M2 = 4.0 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius = 0.20 meter) rotates about a frictionless axle. The acceleration of M2 is 3.5 m/s2. What is the moment of inertia of the pulley?

https://ce.byu.edu/courses/univ/694820121006/media/l10g8.gif


Homework Equations



I=mr^2


The Attempt at a Solution



I have no references in my textbook as to how to approach this sort of problem. I'm not sure where I should even begin.
 
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What would be the acceleration of the system if the pulley was massless?

They give you what the actual acceleration is, so how would you go about accounting for the difference?
 
Couple hints...

Is it fair to say that the pulley has a tangential acceleration equal to the acceleration of the system? (consisting of M1 and M2)

What is the force making the pulley rotate, and how large is it?

M=Ja

Where M is the torque, J is the moment of inertia and a is the angular acceleration
 
It would help to start by drawing a Free Body Diagram (FBD) for each of the masses and the pulley. Then write the equations of motion for each body - two linear equations and one rotational equation, along with the necessary kinematic relations. At that point, it should all be evident how to put it together to find the MMOI of the pulley.
 
I apologize for the late reply. All of what you have said has helped me. Thank you very much. All of you.
 

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