I am really sorry for not seeing the rules of forum before posting ( I am new here). Also thanks for your help. The 'free joint' interpretation gave the right answer.
I have tried this same approach three times and I got the same answer. I can't figure out what's wrong. Btw answer is 12mu/(3+cos2α)
And yes, sorry for my shitty handwriting. If you can't understand the reasoning behind any step then please let me know.
As far I know, in case of non-uniformly rotating frame, everything is same except that we also need to add azimuthal force. And here azimuthal force is not in radial direction.
Why? The fictitious forces are centrifugal, coriolis and azimuthal. Here only centrifugal force is in radial direction. So, the equation should be correct.
Method 1: Simply conserving angular momentum about the the fixed vertical axis and conserving energy gives ##v=3##, which is correct according to my book.
Method 2: Conserving angular momentum when the two rings reach distance ##x## from the centre gives
##(0.01+2x^2) \omega =0.9##
Also in the...