Question

If a point $\left(P\right)$ moves along a circle with constant speed. Ratio of its angular speed wrt any point $\left(O\right)$ on circumference to angular speed wrt centre $\left(C\right)$ of the circle is

• A. $2$
• B. $0.5$
• C. $5$
• D. $50$

Answer 1

The correct option is B $0.5$



Let, $O$ be a point on a circle and $P$ be the position of the particle at any time $t$.
If $\angle POA=\theta$, then $\angle PCA=2\theta$
$(\because \angle PCA$ is exterior angle to triangle $\Delta POC)$
Here, C is the centre of the circle.

Angular velocity of $P$ about $O$ is
${\omega }_0=\frac{d\theta }{dt}$
and
Angular velocity of $P$ about $C$ is,
${\omega }_c=\frac{d}{dt}\left(2\theta \right)=2\frac{d\theta }{dt}$

$\Rightarrow {\omega }_c=2{\omega }_o$