A particle moves through angular displacement ( \theta ) on... | Physics | SolveeIt

A particle moves through angular displacement $\theta$ on a circular path of radius $r$ . The linear displacement will be :

$2r \sin(\theta /2)$

$2r\,\cos(\theta /2)$

$2r\,\ tan(\theta /2)$

$2r\,\cot(\theta /2)$

Answer

$2r \sin(\theta /2)$

Explanation

$\Delta \vec{ r }=\vec{ r }_{2}-\vec{ r }_{1}$ ,
where $r_{2}=r_{1}=r$

Hence, $\Delta r=\sqrt{r_{2}^{2}+r_{1}^{2}-2 r_{2} r_{1} \cos \theta}$
$=2 r \sin \frac{\theta}{2}$

Physics Question on Uniform Circular Motion