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  4. A particle P is moving in a circle of the radius r with a uniform speed v . C is the centre of the circle and AB is the diameter. The angular velocity of P about A and C is in the ratio

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Q. A particle $P$ is moving in a circle of the radius $r$ with a uniform speed $v$ . $C$ is the centre of the circle and $AB$ is the diameter. The angular velocity of $P$ about $A$ and $C$ is in the ratio

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
From properties of $\Delta $
If $\angle CAP=\theta $
then $\angle BCP=2 \, \theta $
$\omega _{A} = \frac{d \theta }{d t}$
$\omega _{C} = 2 \frac{d \theta }{d t}$
$\omega _{A} : \omega _{C} = 1 : 2$