Rotation question. Please Im so confused

[carbon_mc]

Rotation question. Plz please please help. I am so confused

Homework Statement

Two masses m1 and m2 are connected by light cables to the perimeters of two cylinders of radii r1 and r2 respectively, as shown in the diagram above. The cylinders are rigidly connected to each other but are free to rotate without friction on a common axle. The moment of inertia of the pair of cylinders is I = 45 kg.m2. Also r1 = 0.5 meter, r2 = 1.5 meter and m1 = 20kg.
a) Determine m2 such that the system remain in equilibrium

Then the mass m2 is removed and the system is released from rest.
b) Determine the angular acceleration of the cylinders
c) Determine the tension in the cable supporting m1
d) Determine the linear speed of m1 at the time it has descended 1 meter.

Homework Equations

I = mr^2

The Attempt at a Solution

a) I tried 2 ways but I don't know which one is right
sum torque of the system = 0
r1 * tension 1 = r2 * tension2
(0.5)(9.8)(20) = (1.5)(9.8)m2
=> m2 = 6.7

or I = sum mass * r^2
=> m2 = 17.7

and for the next parts of the question, I tried but I'm not sure they are right
b) tangential acceleration = g = 9.8
angular acceleration = a/r1 = 9.8/0.5 = 19.6
c) T = mg = (9.8)(0.5) = 4.9
d) I know we use the kinematic equation of $$\theta$$ = $$\omega$$t + 0.5$$\alpha$$t² but since we don't know what t is, i guess we can't substitute it in
any help is appreciated. thanks a lot. I have trimester exam coming up next week

 

[lanedance]

a) I tried 2 ways but I don't know which one is right
sum torque of the system = 0
r1 * tension 1 = r2 * tension2
(0.5)(9.8)(20) = (1.5)(9.8)m2
=> m2 = 6.7

or I = sum mass * r^2
=> m2 = 17.7

a) if the torques sum to zero the system is static equilibrium,... vertical forces are supported by the shaft,

i'm not sure what your are attempting by summing the masses...

and for the next parts of the question, I tried but I'm not sure they are right
b) tangential acceleration = g = 9.8
angular acceleration = a/r1 = 9.8/0.5 = 19.6
c) T = mg = (9.8)(0.5) = 4.9
d) I know we use the kinematic equation of $$\theta$$ = $$\omega$$t + 0.5$$\alpha$$t² but since we don't know what t is, i guess we can't substitute it in
any help is appreciated. thanks a lot. I have trimester exam coming up next week

for b) cut the problem into two FBDs:
- one for the mass, write down the vertical force/acceleration balance (what is unknown?)
- the other for the cylinder, write down a torque / angular accerlation balance

connect the 2 systems through the tension in the string & c) & d) will follow