A thin uniform circular disc of mass `M` and radius `R` is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with an angular velocity `omega`. Now two particles each of mass `m` are placed on its perimeter along a diameter along a diameter. Find the new angular velocity. If `m=M//2`, find the percentage change in the angular velocity.

Explanation

As there is no external torque, hence by the conservation of angular momentum
`I_(1)omega_(1)=I_(2)omega_(2)`
`(1)/(2)MR^(2)omega=((1)/(2)MR^(2)+mR^(2)xx2)omega'`
`omega'=(Momega)/(M+4m)`
If `m=(M)/(2), omega'=(Momega)/(M+4xx(M)/(2))=(omega)/(3)`
Percentage change in the angular velocity
` =((omega)/(3)=omega)/(omega)xx100=-66.7%`
`66.7%` decrease.