A uniform solid disk of radius 12cm and mass 6kg is free to rotate about a fixed

Question

A uniform solid disk of radius 12cm and mass 6kg is free to rotate about a fixed frictionless axis through its center. It is not moving. An identical second disk has translational speed of 12 m/s(no rotation). The two disks hit and stick together at their rims. What is the rotational speed of of the two disk system after they stick together? (No translational speed since the axis is fixed)

** I saw a solution to this question that didn't look quite right to me. In that solution it looked like the person solved for angular momentum of the disk that was moving but not rotating towards the spinning disk. I am having trouble in setting this problem up. There is no distance defined between the 2 disks. Shouldn't I set up the initial momentum as p=mv since it is translational motion? I would like to see the steps in how to solve this problem with explanations. Thanks.**

Explanation / Answer

see there is no external torque in the 2 disk system so angular momentum is conserved.

but there is external force between them due to fixed hinge force so linear momentum is not conserved.

so you have to deal with conservation of angular momentum as d(torque)/dt=angular momentum=0

hence initial momentum = final momentum.

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