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Question

# Two discs of moment of inertia I1 and I2 about their respective axes which are passing through centre and perpendicular to surface, rotating with angular frequencies ω1 and ω2 respectively, are brought into contact face to face with their axes of rotation coincident. The angular frequency of the composite disc will be

A
I1ω1I2ω2I1I2
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B
I1ω1+I2ω2I1+I2
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C
I2ω1+I1ω2I1+I2
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D
I2ω1I1ω2I1I2
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Solution

## The correct option is B I1ω1+I2ω2I1+I2Before the discs are placed in contact, total initial angular momentum of the two discs, Li=I1ω1+I2ω2 Since the 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 Ic of the composite system will be equal to the sum of their individual moments of inertia, i.e. Ic=I1+I2 If ωc is the angular frequency of the composite system, the final angular momentum of the system, Lf=Icωc=(I1+I2)ωc Since no external torque acts on the system, so we can apply conservation of angular momentum. By the law of conservation of angular momentum, ∴Lf=Li (I1+I2)ωc=I1ω1+I2ω2 ∴ωc=I1ω1+I2ω2I1+I2 Hence, option (B) is correct.

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