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  4. A hoop rolls on a horizontal ground without slipping with linear speed v. Speed of a particle P on the circumference of the hoop at angle θ is <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/b0e49a076b9a3fcf9061b0f07b6e2799-.png />

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Q. A hoop rolls on a horizontal ground without slipping with linear speed $v$. Speed of a particle $P$ on the circumference of the hoop at angle $\theta$ is
image

System of Particles and Rotational Motion

Solution:

$v_{p}=\sqrt{v^{2}+v^{2}+2vv\,cos\left(180-\theta\right)}$
$\Rightarrow v_{p}=\sqrt{2v^{2}\left[1-cos\,\theta\right]}$
$=2v\, sin \, \left(\theta/ 2\right)$
image