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