Two disc of moments of inertia `I_(1) and I_(2)` about their respective axes (normal to the disc and passing through the centre). And rotating with angular speeds `omega_(1)andomega_(2)` are brought into contact face to face with their axes of rotation coincident.
What is the angular speed of the two-disc system?

Explanation

Here, total initial angular momentum of the two discs `L_(1)=I_(1)omega_(1)+I_(2)omega_(2)`
Under, the given conditions, moment of intertia of the two disc system = `(I_(1)+I_(2))`
If `omega` is angular speed of the combined system, the final angular momentum of the system
`L_(2)=(I_(1)+I_(2))omega`
As no external torque is involved in this exercise, therefore, `L_(2)=L_(1)`
`(I_(1)+I_(2))omega=I_(1)omega_(1)+I_(2)omega_(2)`
`omega=(I_(1)omega_(1)+I_(2)omega_(2))/(I_(1)+I_(2))`