A wheel is rotating at an angular speed `omega` about its axis which is kept vertical. An identical wheel initially at rest is gently dropped into the same axle and the two wheels start rotating with a common angular speed. Find this common angular speed.

Explanation

Let the moment of inertia of the wheel abut the axis be I. Initially the first wheel is rotating at the angulr speed `omega` about the axle and the second wheel is at rest. Take both the wheels together as the system. The total angular momentum of the system before the coupling is `Iomega+0=Iomega`. When the second wheel is droipped into the axle, the two wheels slip on each other and exert forces of friction. The forces of friction have torques about teh axis of rotation but these ar torques of interN/Al forces. No exterN/Al torque is aplied on the two wheel system and hence the angular momentum of the system remains unchanged. If the common angular speed is `omega` the total angular momentum of the two wheel system is `2Iomega` after the coupling. thus,
`Iomega=2Iomega`
`or omega'=omega/2`