A thin uniform circular disc of mass `M` and radius `R` is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity `omega`. Another disc of the same dimensions but of mass `M//4 `is placed gently on the first disc coaxially. The angular velocity of the system now is `2omega//sqrt(5)`

Explanation

`tau=(dvecL)/(dt)`
Since, `vectau =0, vecL`= const.

`therefore I_(1)omega_(1) = I_(2)omega_(2), I_(1) = 1/2MR^(2),omega_(1)=omega`
`I_(2)=1/2MR^(2) +1/2M/4 R^(2) = 5/8 MR^(2)`
`omega_(2) =(I_(1)omega_(1))/I_(2) =(1/2MR^(2) xx omega)/(5/8 MR^(2)) =8/(2 xx 5) omega = 4/5 omega`