For rotational motion, use **DID
TASC**

- Diagram and coordinate system
- Isolate the system
- Draw all forces acting
- Take components
- Apply
**F**=m**a**and/or**τ**= I**α**origin dependent! and constraints, if needed. - Solve
- 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
90^{o}: 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:

I_{1} = I_{cm} + Mh^{2} =
½ MR^{2} + Mh^{2} ≈ Mh^{2}

The total moment of inertia is: I = 2Mh^{2}

The angular acceleration becomes: α
= r T/(2 M h^{2})