Pulley w/ 3 Masses Homework: Find Linear Acceleration

[aszymans]

Homework Statement

An green hoop with mass mh = 2.4 kg and radius Rh = 0.12 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.4 kg and radius Rd = 0.11 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat horizontal surface that rolls without slipping and has mass ms = 4.2 kg and radius Rs = 0.25 m. The system is released from rest.

1)What is magnitude of the linear acceleration of the hoop?

Homework Equations

The Attempt at a Solution

I have no idea, would love someone to explain all the very elementary steps, we have never even looked at taking the mass of the pulley into account!

 

[Doc Al]

How would you solve it if the pulley were massless?