An Atwood machine is constructed using a hoop with spokes of negligible mass. The 2.3 kg mass of the pulley is concentrated on its rim which is a distance 23.5 cm from the axle. The mass on the right is 1 kg and on the left is 1.65 kg.

What is the magnitude of the linear acceleration a of the hanging masses?

Explanation:

Since the pulley has a mass concentrated on its rim, the pulley can be considered as a ring.

The moment of inertia of a ring is

The mass on the left is heavier, that is the pulley is rotating counterclockwise.

By Newton's Second Law, the net torque is equal to moment of inertia times angular acceleration.

Here, the net torque is the sum of the weight on the left and the weight on the right.

Applying Newton's Second Law gives the angular acceleration

The relation between angular acceleration and linear acceleration is

Then, the linear acceleration of the masses is