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A particle $P$ is moving in a circle of radius ' $a$ ' with a uniform speed $v . C$ is the centre of the circle and $A B$ is a diameter. When passing through $B$ the angular velocity of $P$ about $A$ and $C$ are in the ratio
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1:2
Angular velocity of particle $P$ about point $A$,
$\omega_A=\frac{v}{r_{A B}}=\frac{v}{2 r}$
Angular velocity of particle $P$ about point $C$,
$\begin{aligned} & \omega_C=\frac{v}{r_{B C}^r}=\frac{v}{r} \\ & \text { Ratio } \frac{\omega_A}{\omega_C}=\frac{v / 2 r}{v / r}=\frac{1}{2} .\end{aligned}$
$\omega_A=\frac{v}{r_{A B}}=\frac{v}{2 r}$
Angular velocity of particle $P$ about point $C$,
$\begin{aligned} & \omega_C=\frac{v}{r_{B C}^r}=\frac{v}{r} \\ & \text { Ratio } \frac{\omega_A}{\omega_C}=\frac{v / 2 r}{v / r}=\frac{1}{2} .\end{aligned}$
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