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

Question

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 (A) 1: 1 (B) 1: 2 (C) 2: 1 (D) 4: 1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-sei6da5omuvjnfxi.jpg" /> From properties of Δ If angle CAP=θ then angle BCP=2 θ ω A = (d θ /d t) ω C = 2 (d θ /d t) ω A: ω C = 1: 2

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 $A B$ is the diameter. The angular velocity of $P$ about $A$ and $C$ is in the ratio

$1 : 1$

$1 : 2$

$2 : 1$

$4 : 1$

From properties of $Δ$
If $∠ C A P = θ$
then $∠ BCP = 2 θ$
$ω_{A} = \frac{d θ}{d t}$
$ω_{C} = 2 \frac{d θ}{d t}$
$ω_{A} : ω_{C} = 1 : 2$

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

1:1

1:2

2:1

4:1