Rotational Motion Question 8
Question 8 - 2024 (30 Jan Shift 2)
Two discs of moment of inertia $I _1=4 kg m^{2}$ and $I _2=2 kg m^{2}$ about their central axes $\&$ normal to their planes, rotating with angular speeds $10 rad / s \& 4 rad / s$ respectively are brought into contact face to face with their axe of rotation coincident. The loss in kinetic energy of the system in the process is J.
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Answer: (24)
Solution:
$I _1 \omega _1+I _2 \omega _2=\left(I _1+I _2\right) \omega _0$ (C.O.A.M. )
gives $\omega _0=8 rad / s$
$E _1=\frac{1}{2} I _1 \omega _1^{2}+\frac{1}{2} I _2 \omega _2^{2}=216 J$
$E _2=\frac{1}{2}\left(I _1+I _2\right) \omega _0^{2}=192 J$
$\therefore \Delta E=24 J$
