A weightless and unstretchable string has one end fixed at the point A.
The string passes under a movable pulley Q (of radius R/2
but negligible mass and moment of inertial) carrying a mass M_{2}.
Then the string passes over a fixed pulley P of moment of inertia
I_{3}, and finally the string is attached to mass
M_{1} at its other end, as shown. The pulleys have frictionless
axles but the string doesn't slip on their rims.

What should be the relation between M_{1} and
M_{2} for static equilibrium?
M_{1}/M_{2} =

When M_{1} moves down 1 meter, how far up does
M_{2} move?
m

Now consider the acceleration of the system when the static equilibrium
condition of part (a) above does not hold.

Answer the following in terms of M_{1} (M1),
M_{2} (M2),
I_{3} (I3), the tensions T_{1} (T1),
T_{2} (T2), and
T_{3} (T3) and g (g).
For example, the answer to (c) is: M1*g-T1

What is the net downward force on M_{1}?

What is the net counterclockwise torque on the fixed pulley P?

What is the net counterclockwise torque on the lower pulley Q?

What can you say about the relation between T_{2} and
T_{3}?
T_{3}/T_{2} =

Why?

What is the net upward force on the M_{2} and pulley Q
combination?

Proceed to solve for the acceleration of
M_{1} in terms of the mass M_{2},
moment of inertia I_{3}, radius R, and
g.