(Solution) - Two objects are attached to ropes that are attached to wheels -(2025 Original AI-Free Solution)

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Two objects are attached to ropes that are attached to wheels on a common axle as shown in Figure. The total moment of inertia of the two wheels is 40 kg?m2. The radii of the wheels are R1 = 1.2 m and R2 = 0.4 m.
(a) If m1 = 24 kg, find m2 such that there is no angular acceleration of the wheels.
(b) If 12 kg is gently added to the top of m1, find the angular acceleration of the wheels and the tensions in the ropes.