Let's apply Newton's Second Law to two cylindrical masses on a rotating
massless platform. We determine the angular acceleration in terms of:
M, the mass of each cylinder;
h, the distance from the rotation axis to each cylinder;
T, the tension applied by the string;
r, the radius of the axle.
We assume that the radius of each cylinder is small compared to h.
The only torque comes from the tension in the string.
Using τ = r × F and the fact that the angle between r and T is 90o: τ = rT
Solving Newton's Second Law gives α = r T/I.
Each cylinder rotates about the center of the platform. By the parallel axis theorem, each cylinder has a rotational inertia:
I1 = Icm + Mh2 = ½ MR2 + Mh2 ≈ Mh2
The total moment of inertia is: I = 2Mh2
The angular acceleration becomes: α
= r T/(2 M h2)