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A hoop rolls on a horizontal ground with...

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 :

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For rolling without slipping, `V_(CM)=romega` The Velocity of P is the resultant of CM velocity and the tangential velocity `romega`due to clockwise rotation velocity of )`""^2`=`(V_(CM)-romegacostheta)^2+(romega sin theta)^2`=`V_(CM)^(2)(1-costheta)^2+V^2 sin^2 theta`(as `romega=V_(CM)`=`(4V_(CM)^(2)sin^2)(theta)/2``rArr velocity of P=(2V_(CM)sin)theta/2`.

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