Undergrad Energy Transfer Between Inertia Wheels

[DrunkElk1601]

TL;DR

One flywheel is spinning and a 2nd flywheel is at rest. A clutch connects the shafts. What's the final rpm?

Been 20 years since college physics. I have a problem where there are basically two inertia wheels on separate shafts coupled by a clutch. One wheel is spinning and the other is at rest. The clutch engages and connects the shafts. What's the final rpm of both wheels? I'm struggling to find a similar problem to use an example. I know the radius, KE, moment of inertia, rpm, clutch engagement time, etc. but I'm not sure how to determine the final torque because it's not clear how to find the final rpm. If you would please describe the general approach or link a similar problem I'd appreciate it.

 

[Merlin3189]

Conservation of angular momentum.

 

[Dale]

If the bearings are good then you can use conservation of angular momentum