Hello. Here is my problem that I am stuck on. Imust be missing something when I

Question

Hello. Here is my problem that I am stuck on. Imust be missing something when I try to solve. I always endup with too many unknown variables and not enough equations tosolve them. Any help would be awesome.
Two objects are attached to ropes that are attached to wheelson a common axle as shown below. The two wheels are glued togetherso that they form a single object. The total moment of inertia ofthe two wheels is 43 kg ·m2. The radii of the wheels are R1 =1.1 m and R2 =0.10 m. (a) If m1 = 24 kg, findm2 such that there is no angular accelerationof the wheels.
(b) If 12 kg is gently added to the top of m1,find the angular acceleration of the wheels.
Find the tension in the rope holding m1.
Find the tension in the rope holdingm2.

Explanation / Answer

m1 g R1 = m2 gR2   when there is no angularacceleration Let M1 be m1 + 12 kg T1 - T2 = I    where T is the tension in the ropes supporting the masses M1 g - T1 = M1a1       the accelerationof M1 T2 - m2 g = m2a2        theacceleration of mass m2 T2 - T1 + (M1 -m2) g = ( M1 a1 + m2a2) =  ( M1 R1 + m2 R2)     adding the last two equations Now substitute T1 - T2 = I  and you can solve for T2 - T1 + (M1 -m2) g = ( M1 a1 + m2a2) =  ( M1 R1 + m2 R2)     adding the last two equations Now substitute T1 - T2 = I  and you can solve for

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