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  4. A uniform disc is spinning about geometrical axis in free space. Its temperature is increased by ∆T. The fractional change in its angular velocity is (α is coefficient of linear expansion)

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Q. A uniform disc is spinning about geometrical axis in free space. Its temperature is increased by ∆T. The fractional change in its angular velocity is ($\alpha$ is coefficient of linear expansion)

Solution:

Angular momentum remains constant
$I \omega = const.$
$\frac {\Delta l}{l}+\frac {\Delta \omega}{\omega}=0$
$2 \alpha \Delta T +\frac {\Delta \omega}{\omega}=0 \therefore \frac {\Delta \omega}{\omega} = -2 \alpha \Delta T$