Establish a relation between angular velocity and time period. - Vidyadip

Question

Establish a relation between angular velocity and time period.

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Answer

We know that angular velocity $\omega=\frac{\Delta\theta}{\Delta\text{t}}$
For motion with uniform angular velocity, in one complete revolution $\Delta\theta=2\pi$ radian and $\Delta\text{t}=\text{T s},$ hence
$\omega=\frac{2\pi}{\text{T}}$ or $\text{T}=\frac{2\pi}{\omega}.$

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