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

[wesDOT]

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.

 

[LowlyPion]

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?

 

[Ofey]

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

 

[Dr.D]

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.

 

[wesDOT]

I apologize for the late reply. All of what you have said has helped me. Thank you very much. All of you.