Two discs of moment of inertia and about their central axes and normal to their planes, rotating with angular speeds 10 rad/s and 4 rad/s respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic en

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Solution

Q.
Two discs of moment of inertia $I_{1} = 4$ $k g m^{2}$ and $I_{2} = 2$ $k g m^{2}$ about their central axes and normal to their planes, rotating with angular speeds 10 rad/s and 4 rad/s respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is ________ J. [2024]

Ans.
(24)   Here angular momentum will remain conserve

$L = I ω$

   $L_{i} = L_{f}$

$4 \times 10 + 2 \times 4 = (6) ω$

   $48 = 6 ω$

   $ω = 8 rad / \sec$

   $Δ K E = K E_{f} - K E_{i}$

$Δ K = \frac{1}{2} (6) {(8)}^{2} - [(\frac{1}{2} 4 \times 10^{2}) + (\frac{1}{2} (2) \times {(4)}^{2})]$

   $Δ K = 192 - 216$

   $Δ K = - 24 J$

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