I think that angular acceleration of the bobbin created is to be found out here. The dimension of angular velocity does not match with that of the quantity (depending on g/R) given in the answer..
Here the gravitational pull will produce a torque and that torque will generate angular acceleration of the bobbin.
If a represents the angular acceleration then
I×a = mg×R/2= the torque
=>3 mR^2a=R/2×mg
=>a=g/(2×3R) rad/sec^2