Wheel-Hub System and Angular Acceleration

[etherealcalc]

Homework Statement

A wheel of radius r₁=0.8m and hub of radius r₂=0.4m is shown in the diagram. Two masses are hung from the wheel-hub system. The mass m₂, on the left, is hung from the hub. The mass m₁ is hung from the wheel. The system is in equilibrium. The moment of inertia for the disk-hub system is I=1.34 kg m².

If m1=0.88 kg is large enough for the system to rotate, when m₂=1.6kg, what is the magnitude of the acceleration of mass m₂?

A. a=3.9 m/s²
B. a= 0.37 m/s²
C. a= 0.19 m/s²

Homework Equations

τ= Fr=Iα
F=mg
αr=a

The Attempt at a Solution

I thought this would work: Fr=Iα
(1.6*9.8-.88*9.8)(0.4)=1.34(a/0.4)
14.272(0.4)(0.4)/1.34=a
a=1.70
I also thought that maybe I should have just focused on the force from m2, but that wasn't it either (a=1.87)

 

[Enelafoxa]

The Arm of m1g and m2g are different. You Should try again and read the problem carefully.

 

[haruspex]

In addition to Enelafoxa's point, the two masses also need a forces to accelerate them.
Create variables for the string tensions and consider the forces and accelerations of all three bodies (the two masses and the disk+hub) separately.