What is Instantaneous Angular Acceleration?
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What is Instantaneous Angular Acceleration?

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It is the limit of average angular acceleration as $\Delta \mathrm{t}$ approaches zero, i.e.,

$\vec{\alpha}=\lim _{\Delta t \rightarrow 0} \frac{\Delta \vec{\omega}}{\Delta t}=\frac{\mathrm{d} \vec{\omega}}{\mathrm{dt}}$

since $\vec{\omega}=\frac{\mathrm{d} \vec{\theta}}{\mathrm{dt}}, \quad \therefore \vec{\alpha}=\frac{\mathrm{d} \vec{\omega}}{\mathrm{dt}}=\frac{\mathrm{d}^{2} \vec{\theta}}{\mathrm{dt}^{2}}, \quad$

Also$\quad \vec{\alpha}=\omega \frac{\mathrm{d} \vec{\omega}}{\mathrm{d} \theta}$

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