Two pulleys (one is a combination of two cylinders), and hanging mass.

[9997]

Homework Statement

Two pulleys are mounted on fixed axles that have negligible friction. The small pulley has a moment of inertia of 9.0 kgm^2, and is made of up of two cylinders wielded together, one of radius 7.0 cm, and one of radius 15.0 cm. The large pulley has a radius of 41.0 cm, and a moment of inertia of 84 kgm^2; he pulleys are coupled together using a light belt. A 7.00 kg mass hangs from the smaller pulley by a rope that is wound around the smaller cylinder. The system is initially at rest, and the mass is then let go, and begins to fall.

a) Find the acceleration of the mass.
b) Find the tension in the rope.
c) Is the tension in the belt the same everywhere?

Homework Equations

Dynamics equations (summation of forces).
Torque = Iα

The Attempt at a Solution

I'm actually a bit lost. Our textbook is really bad, and I can't seem to figure out how to solve this question. I've looked online for other resources, but can't seem to find any.

Any help is appreciated! Thank you.

 

[Simon Bridge]

You are doing well - free body diagrams for each part of the problem.

i.e. for the mass:
mg-T=ma (I like to avoid subscripts)

What to do about the wheels right?
You have the right equation - draw the wheels separately and draw the torques on them.