Applying Newton's Second Law

For rotational motion, use DID TASC
  1. Diagram and coordinate system
  2. Isolate the system
  3. Draw all forces acting
  4. Take components
  5. Apply F=ma   and/or   τ = I α  origin dependent!  and constraints, if needed.
  6. Solve
  7. Check!

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)