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  4. 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

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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

Motion in a Plane

Solution:

Angular velocity of particle $P$ about point $A$,
$\omega_{A} =\frac{v}{r_{AB}} =\frac{v}{2r}$
Angular velocity of particle $P$ about point $C$,
image
$\omega_{C} =\frac{v}{r_{AB}} =\frac{v}{r}$
Ratio $\frac{\omega_{A}}{\omega_{C}} =\frac{v/2r}{v/r}=\frac{1}{2}$