The device shown in Fig. rotates on the vertical axle as shown. The frame has negligible mass as compared to the four masses each of mass `m`. Initial angular velocity of the system is `omega_(0)`. Due to an internal mechanism the spokes in the frame lengthen so that the radii of the masses become `2a`. Initially, it was a. What will be the new angular velocity of the system?

Explanation

The will be no torque on the system if we ignore frictional torque at the axle. Therefore, the angular momentum of the system is conserved.
`vecL_("initial")=vecL_("final")`
`I_("initial")omega_(0)=I_("final")omega`
`4ma^(2) omega_(0)=4m(2a)^(2)omega`
from which we have `omega=(omega_(0))/4`