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

Moderate

Solution

Angular velocity of particle P about point A,
$ω_{A} = \frac{v}{r_{AB}} = \frac{v}{2 r}$
Angular velocity of particle P about point C,
$ω_{c} = \frac{v}{r_{BC}} = \frac{v}{r}$
Ratio $\frac{ω_{A}}{ω_{C}} = \frac{\frac{v}{2 r}}{\frac{v}{r}} = \frac{1}{2}$

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