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  4. A particle is moving with a uniform speed v in a circular path of radius r with the centre at O. When the particle moves from a point P to Q on the circle such that angle POQ=θ, then the magnitude of the change in velocity is

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Q. A particle is moving with a uniform speed $v$ in a circular path of radius $r$ with the centre at $O$. When the particle moves from a point $P$ to $Q$ on the circle such that $\angle POQ=\theta$, then the magnitude of the change in velocity is

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Solution:

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$\therefore $ Change in magnitude of velocity
$|\Delta v | =\sqrt{v^{2}+v^{2}-2 v^{2} \cos \theta}$
$=2 v \sin \frac{\theta}{2}$