Two discs of moments of inertia I1 and I2 about their respective axes, rotating with angular frequencies ω1and ω2  respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be

The initial angular momentum of the two discsL1=I1ω1+I2ω2The moment of inertia IC. of the composite system will beIC=I1+I2If ωCto" be the angular frequency of the composite system, then the final angular momentum L2, is given byL2=Icωc=I1+I2ωcApplying the law of conservation of angular momentum, we haveI1+I2ωC=ICω1+I2ω2or ωC=I1ω1+I2ω2I1+I2