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Systems of Particles and Rotational Motion — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsSystems of Particles and Rotational Motion2 Marks
Question
If angular momentum is conserved in a system whose moment of inertia is decreased, will its rotational kinetic energy be also conserved? Explain.
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Answer

No, rotational KE is not conserved, as
$\text{I}_1\omega_1=\text{I}_2\omega_2$
$\text{I}^2_1\omega^2_1=\text{I}^2_2\omega^2_2$
$\text{I}_1\Big(\frac{1}{2}\text{I}_1\omega^2_1\Big)=\text{I}_2\Big(\frac{1}{2}\text{I}_2\omega^2_2\Big)$
$\text{I}_1\text{K}_1=\text{I}_2\text{K}_2$
If I2 < I1 then K2 > K1
i.e. when MI decreases, rotational KE increases.

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