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Instantaneous Axis of Rotation

Two discs of ...

Question

Two discs of moments of inertia $I_{1}$ and $I_{2}$ about their transverse axes,rotating with angular frequency $ω_{1}$ and $ω_{2}$ respectively are brought into contact with their axes of rotation coincident .Find the angular frequency of their composite disc.

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Solution

Applying conservation of Angular momentum of system
initial momentum = final momentum
$I_{1} w_{1} + I_{2} w_{2} = (I_{1} + I_{2}) w$
$w = \frac{I_{1} w_{1} + I_{2} w_{2}}{I_{1} + I_{2}}$

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