A particle P is moving in a circle of radius ‘a ’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio

Question

A particle P is moving in a circle of radius ‘a ’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio (A) 1:1 (B) 1 :2 (C) 2: 1 (D) 4: 1

Tardigrade Admin · Accepted Answer

Angular velocity of particle P about point A, ωA =(v/rAB) =(v/2r) Angular velocity of particle P about point C, <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/67673460d2a97fcef24e4c60561f24c5-.jpeg" /> ωC =(v/rAB) =(v/r) Ratio (ωA/ωC) =(v/2r/v/r)=(1/2)

Q. A particle P is moving in a circle of radius ‘a ’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio

$1 : 1$

$1 : 2$

$2 : 1$

$4 : 1$

Angular velocity of particle $P$ about point $A$ ,

$ω_{A} = \frac{v}{r _{A B}} = \frac{v}{2 r}$

Angular velocity of particle $P$ about point $C$ ,

$ω_{C} = \frac{v}{r _{A B}} = \frac{v}{r}$

Ratio $\frac{ω _{A}}{ω _{C}} = \frac{v /2 r}{v / r} = \frac{1}{2}$