Question
A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by $1\%$. Its angular speed
✓
Answer
volume of spherical body, $V=\frac{4}{3} \pi R^{3}$
$\Rightarrow \frac{\Delta V}{V}=3 \frac{\Delta R}{R}$
$\Rightarrow \frac{\Delta R}{R}=0.33$
As there is no external torque angular momentum is conserved, $L=I \omega$
$\Rightarrow L=\frac{2}{5} M R^{2} \omega$
$\Rightarrow \frac{\Delta L}{L}=2 \frac{\Delta R}{R}+\frac{\Delta \omega}{\omega}$
since, $\frac{\Delta L}{L}=0$ as the magnitude is constant.
$\Rightarrow \frac{\Delta \omega}{\omega}=-2 \frac{\Delta R}{R}$
Therefore, $\omega$ decreases by $0.67 \%$
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