calculating initial downward acceleration

[husny540]

As shown in the figure, each pulley has radus R and moment of inertia I. Each connected components weight is m. For the middle one m weight is including for the pulley. If the middle one released shows that the initial download acceleration is ((1-2 sin⁡〖θ)〗 mg)/(m+2(m+1/R^2 )〖sin〗^2 α) (In the image the masses are denoted as M1,M2,M,3 but consider all the masses to be m as given the question) Can you help solve this?

 

[tgootee]

Use "conservation of energy" approach, to write the equation.

i.e. Write an expression for the initial potential energy and set it equal to an expression for the potential plus kinetic energy at any time after release.

It's easier than you think. Just start writing the expressions for the energies, from what you know, in terms of what you know, and you will soon have the correct equation to solve.

It's a great approach and is like a "unified theory" for all dynamics (and maybe all classical physics) problems.