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 co-axially. show that angular velocity o fthe system is `4 omega//5`.

Explanation

Initial angular momentum of one disc.
`L = I omega = (1)/(2)MR^(2) omega`
When another disc. Of mass `(M)/(4)` and radius `R` is placed gently on it, total moment of inertia of the combination is
`I' = (1)/(2)MR^(2) + (1)/(2) ((M)/(4))R^(2) = (5)/(8)MR^(2)`
As no external torque has been applied, angular momentum is conserved.
`:. I' omega' = I omega, omega' = (I omega)/(I') = ((1)/(2)MR^(2) omega)/((5)/(8)MR^(2)) = (4)/(5) omega`