Question

A disk (mass of 3 kg, radius 30 cm) is rotating with an angular velocity w1= 5 rad/s. A second disk (mass 2kg, radius 15cm), which is rotating at w= -7 rad/s is dropped on top of the first disk. The disks are dropped so that they share a rotational axis, and they stick together. The moment of inertia of a disk is 1/2mr^2. What is the final angular speed of the two disks?

Answer 1

Moment of inertia of first disk,

  

Moment of inertia of second disk,

  

Since both disks are rotating at a constant angular velocity, the net external torque on thee system is 0.

By the law of conservation of angular momentum, L_{final =} L_initial

Let the final angular velocity of the combined system be

Since the disks share a roational axis, the final moment of inertia of the system will be a sum of the individual Moment of Inertias of the disks.

Hence,