Two discs of moments of inertia I 1 and I 2 about their respective axes, rotating with angular frequencies 
and 
respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be
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: Total initial angular momentum of the two discs is 
When two discs are brought into contact face to face (one on top of the other) and their axes of rotation coincide, the moment of inertia I of the system is equal to the sum of their individual moments of inertia. i.e., 
Let 
be the final angular speed of the system.
The final angular momentum of the system is
As no external torque acts on the system, therefore according to law of conservation of angular momentum, we get
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